How to prove f(n)=O(n) for any integer ⩾1, if f(1)=1 and f(n)=2f(⌊n/2⌋)+1 for n⩾2?

Do you need induction? If so, how do you do it?

Consider the following LP formulation of the modified Dog Food example you learned in class (by adding gruel 5). The objective coefficients represent unit costs ($ per 16 oz) for the gruels. The RHS’s represent the nutrition requirements (measured in oz). MIN 4 G1 + 6 G2 + 3 G3 + 2 G4 + 5 G5 SUBJECT TO 2) 3 G1 + 5 G2 + 2 G3 + 3 G4 + 4 G5 >= 3 (Protein Req.) 3) 7 G1 + 4 G2 + 2 G3 + 8 G4 + 2 G5 >= 5 (Carbohydrate Req.) 4) 5 G1 + 6 G2 + 6 G3 + 2 G4 + 4 G5 >= 4 (Fat Req.) 5) G1 + G2 + G3 + G4 + G5 = 1 (Total %) END Below is the LINDO output of the problem. OBJECTIVE FUNCTION VALUE 1) 3.000000 VARIABLE VALUE REDUCED COST G1 0.000000 0.500000 G2 0.166667 0.000000 G3 0.333333 0.000000 G4 0.500000 0.000000 G5 0.000000 1.000000 ROW SLACK OR SURPLUS DUAL PRICES 2) 0.000000 -1.000000 3) 0.333333 0.000000 4) 0.000000 -0.500000 5) 0.000000 2.000000 RANGES IN WHICH THE BASIS IS UNCHANGED: OBJ COEFFICIENT RANGES VARIABLE CURRENT ALLOWABLE ALLOWABLE COEF INCREASE DECREASE G1 4.000000 INFINITY 0.500000 G2 6.000000 2.000000 3.000000 G3 3.000000 1.000000 3.000000 G4 2.000000 2.000000 INFINITY G5 5.000000 INFINITY 1.000000 RIGHTHAND SIDE RANGES ROW CURRENT ALLOWABLE ALLOWABLE RHS INCREASE DECREASE 2 3.000000 1.000000 0.500000 3 5.000000 0.333333 INFINITY 4 4.000000 0.250000 2.000000 5 1.000000 0.142857 0.038462 Consider yourself as the dog food producer. Answer the following questions based on the LP output:

1. (1pts) What is the minimum cost to make such dog food?

2. (3pts) The dog food buyer is willing to pay $0.5 more if you increase the fat by 1 oz in the 16 oz can of dog food and keep other nutrients unchanged. Do you want to take the offer? Explain.

3. (2pts) Among all gruels, which is least attractive to you? Explain.

4. (3pts) If the gruel 1 seller wants to offer you 10% discount on gruel 1, will you be interested in buying the gruel 1? If not, what would be the attractive price for gruel 1? Explain.

5. (4pts) If the unit price (cost) of gruel 2, gruel 3, and gruel 5 increase by $0.5, respectively, and that of gruel 4 decreases by $0.5, do you want to change the current dog food mix? Will the minimum cost for the dog food change? If so, by how much? Show your calculations.

6. (3pts) Would you be interested in buying gruel 6 that sells for $4 per 16 oz, which contains 3 oz of protein, 6 oz of carbohydrate, and 7 oz of fat? Show your calculations.

7. (4pts) If the dog food buyer requests to increase the protein level by 0.6 oz in exchange for reducing the fat level by 0.7 oz, would you take this offer? Explain and show your calculation.

QUESTION 1 Heineken beer is sold predominantly in liquor stores. Liquor stores can be considered to be ___________ stores as they have a narrow, but deep product range.

1 Internet 2 discount 3 speciality 4 department

QUESTION 2 Heineken is recognised as the world’s most valuable international premium beer brand. This means that Heineken has many loyal consumers. During which phase of brand loyalty would consumers refuse to accept a substitute?

1 Brand insistence 2 Brand preference 3 Brand recognition 4 Brand refusal

QUESTION 3 Heineken is recognised as the world’s most valuable international premium beer brand. Which one of the following is an advantage of having a strong brand for Heineken? 1 Facilitates the identification of products when purchasing. 2 Assures consumers of a quality standard they can count on. 3 Serves as a warning against products that do not meet consumer standards. 4 Provides the foundation stone of the marketing communication strategy.

QUESTION 4 Janika bakes cookies and rusks which she sells to family and friends for pocket money. She charges R29,99 for a small bag of cookies and R39,99 for rusks. She believes this price makes her cookies and rusks appear to be better value for money than charging R30 or R40 respectively. Which adaption to the final price of her cookies and rusks does Janika use?

1 Bait prices 2 Odd prices 3 Market-price level prices 4 Market-penetration prices

QUESTION 5 Products such as laptops adhere to market price strategies. For brands, such as Apple and Mac, who have successfully differentiated their products, there is some price discretion as consumers perceive the products to be unique and do not mind paying more for them. During which product-life cycle would one typically find such types of price decisions?

1 Introductory phase 2 Growth phase 3 Maturity phase 4 Declining phase

QUESTION 6 _______________ can be defined as creating a need-satisfying product or service.   

1 Decisions 2 Opportunities 3 Development 4 Transferring

QUESTION 7 Lexus cars are advertised in prestigious magazines and sold at exclusive dealerships at a much higher price than that of the Toyota RAV4. This represents the ___________ .

1 total product 2 generic brand 3 product image 4 need-satisfying product

QUESTION 8 Which one of the following types of research would be chosen if a company needs to conduct problem-identification research?

1 Segmentation research 2 Product research 3 Pricing research 4 Image research

QUESTION 9 The various brands of beer that SABMiller markets include: Castle Lager, Castle Light, Carling Black Label and Hansa Pilsner, to name a few. The packaging for these various brands is very similar with only the individual labels being different. SABMiller is making use of _____________ packaging.

1 reusable 2 speciality 3 family 4 economic

QUESTION 10 Mpho is shopping for a new motorbike. He has decided to purchase the new BMW R 1200 GS Adventure. The dealership he has decided to purchase the motorbike from, met his needs with speed and initiative and was able to answer all of his queries. To which dimension of service does this relate?

1 Reliability 2 Responsiveness 3 Assurance 4 Empathy

QUESTION 11 IBM had a better statement of financial position, despite falling behind in sales. Which one of the following best describes the statement of financial position?

1 Can be described as the accrued power of disposal over the products and services used by the business to generate a monetary return. 2 Consists of primarily receipts resulting in the sale of the business’s products and/or services. 3 Reflects all of the possessions of the business as well as the nature and extent of the interests in these possessions. 4 Furnishes details about the manner in which the profit or loss for a particular period was arrived at and how it has been distributed.

QUESTION 12 Which one of the following would appear on IBM’s statement of financial position?

1 Shareholders’ interest 2 Operating profit 3 Returns 4 Provision for tax

QUESTION 13 The __________ of IBM consists primarily of receipts resulting from the sale of its products and/or services.

1 profit 2 income 3 liquidity 4 capital structure

QUESTION 14 IBM’s sales would be indicated on the statement of financial __________ and is also known as ________ income.

1 position; gross 2 position; net 3 performance; net 4 performance; gross

QUESTION 15 The formula for calculating the future value of an original investment is:

FVn = PV (1 + i)n

Where n is:

1 The original investment 2 The future value of the investment 3 The interest rate per period 4 The number of discrete periods over which the investment extends

Read the case study below and then answer questions 16 and 17.

Khanyisile owns a fabric store and offers a curtain-making service to her customers. The industrial machine used to sew the curtains has broken down and Khanyisile needs to decide if it is worth it to replace the machine right now.

A new machine is worth R50 000, but she does not really have the capital at the moment to replace the machine. Her brother owns such a machine and has indicated that he will give it to her now with payment only due in three years. He is willing to let her take the machine for R75 000 at an interest rate of 15% per year.

She has approached you to assist her and you advise her that she will need to look at the present value of the machine before making a decision.

QUESTION 16 Given the high decrease of the discounting factors along with the high interest rates offered on the machine and the long time period she will require to pay off the machines, the following is correct:

1 The lower the interest rate is, the smaller the present value of a given future amount will be. 2 The higher the interest rate is, the bigger the present value of a given future amount will be. 3 The higher the interest rate is, the smaller the present value of a given future amount will be. 4 The lower the interest rate is, the bigger the present value of a given future amount will be.

QUESTION 17 Given the information above, calculate what the machine’s present value would be if Khanyisile decides to accept her brother’s offer.

1 R50 000 2 R49 312.50 3 R114 067.50 4 R56 347.50

QUESTION 18 Which financial ratio is used by providers of loan capital to determine the degree to which a business can meet its debt obligations fully and punctually in the normal course of events?

1 The current ratio 2 The solvency ratio 3 The debt ratio 4 The gearing ratio

QUESTION 19 Rapula is the financial manager of Plastic Fantastic, a plastic container manufacturer. While doing the financial statements, Rapula will need to calculate the return of investment (ROI). In addition to net profit after tax, Rapula will also require ___________ in order to calculate this ratio.

1 sales 2 gross profit margin 3 total assets 4 owners’ equity   

QUESTION 20 The focal points of a budget for an income centre is determined by measuring _______________ .

1 outputs in monetary terms 2 inputs in monetary terms 3 performance in monetary terms 4 inputs and outputs in monetary terms

QUESTION 21 Maintaining the purchasing and supply system of Toyota will occur at the ______________ level of purchasing and supply planning.

1 strategic 2 tactical 3 middle-management 4 operations

QUESTION 22 Supply-chain process integration at Toyota will occur at the ___________ level of purchasing and supply planning.

1 strategic 2 tactical 3 middle-management 4 operations

QUESTION 23 The purpose of Toyota’s purchasing and supply function is not only to provide the right materials, services and equipment, but also to _____________________ .

1 retain the market share by providing products to consumers that satisfy their needs. 2 ensure that they are purchased at a reasonable price, satisfy quality requirements and are received in the correct quantities at the right place and time. 3 manage and select appropriate suppliers who can deliver the required materials within the specified time frames. 4 manage the planning, organising, leading and controlling of all activities relating to the purchasing of materials and services.   

QUESTION 24 In which scenario below would purchasing as a factor in profitability be more critical than usual?

1 When the business is committed to its suppliers. 2 If the price of materials stays constants over time. 3 Where fashion is concerned. 4 Where the final market for the product is not competitive.   

QUESTION 25 Vicki is the regional buyer for Black Cat Pet stores in Gauteng. She prefers to buy a greater volume of cat food at her preferred supplier, Munchkins, as it results in lower inventory levels and lower prices as Munchkins gives her discount for volume orders. This is an advantage of _______________ which is possible with a _________ purchasing and supply structure.

1 standardisation; centralised 2 profit-leverage; centralised 3 volume discounts; decentralised 4 supplier relationships; decentralised

QUESTION 26 Kgaugelo owns an organic food store in Newlands. As the store is new, it is quite small and Kgaugelo does not have a dedicated purchasing and supply manager at the moment. Which one of the following is another factor Kgaugelo will use to determine the importance of the purchasing and supply function?

1 The situation in the supplier market. 2 The hierarchy of the management levels. 3 The quality of the materials required. 4 The speed with which stock needs to be replenished.

QUESTION 27 When it comes to the internal organisation of the purchasing and supply function, ____________ are used when each person takes responsibility for buying a specific material or service.   

1 independent buyers 2 informal structures 3 specialist groups 4 cross-functional teams

QUESTION 28 Which one of the following represents a level at which co-ordination of the purchasing and supply function occurs?

1 Various purchasing and supply activities must be co-ordinated externally in the purchasing and supply function. 2 The purchasing environment (buyers) must be co-ordinated with purchasing activities. 3 The purchasing and supply function must be co-ordinated with other functional management areas. 4 The purchasing and supply function operates independently from other functions and as such, no co-ordination is required.

QUESTION 29 Moses works for Studio Grant, an interior design company who also manufactures custommade pieces for clients. He is the purchasing and supply manager and is responsible for purchasing the materials required to produce these bespoke pieces. Which measure can he adopt to ensure that purchasing and supply objectives are pursued within acceptable standards?

1 Gant graphs 2 Purchasing and supply control 3 Purchasing and supply performance measurements 4 Requisition management

QUESTION 30 Moses uses the control point of price proficiency to determine if purchasing activities are being performed effectively. Which one of the following would he use to determine the effectiveness of price proficiency?

1 The number of orders received late. 2 The number of orders indicated as urgent. 3 The number of orders rejected. 4 The number of discounts negotiated for a specific period.

You are opening a smoothie bar, identify the following:

• Your business market: Blank 1 .
• Provide a specific example for each resource category required to start this type of business: Blank 1, Blank 2, Blank 3, Blank 4 .

1 answer for buisness market and 4 for 2nd bullet

Consider the following time series data.

Formally assess whether usage is a significant predictor of mean interruptions, providing numerical justification (test statistic and
P-value) for your conclusion. Carefully interpret what the estimated model tells you about how
the expected number of interruptions changes as the daily usage changes.

DATA four;
INPUT interruptions usage;
cards;
0 104.2
2 124.6
5 176.3
6 169.3
1 104.6
2 115.8
3 127.8
6 179.4
8 210.5
4 126.7
0 100.5
1 119.5
1 123.8
0 106.4
4 156.7
3 148.2
5 156.2
6 167.3
8 198.2
2 124.6
3 145.9
4 156.2
;
run;

QUESTION 5

1. In a factorial design, a main effect is the

2. 	1.	effect of the interaction between two variables.
   	2.	effect of one independent variable at one level of the other independent variable.
   	3.	effect of one independent variable averaged over the levels of the other independent variable.
   	4.	only effect of interest

QUESTION 11

1. The overall effect of an independent variable ignoring other independent variables is called a(n) ____________.

   	1.	collapsed effect
   	2.	interaction
   	3.	main effect
   	4.	omnibus effect

When graphing the results of a complex design, the dependent variable is always placed