To celebrate their Queen’s 90^th birthday, the country of Wonderland has decided to bake the world’s largest cake. The main ingredient of the cake will be flour. It has been estimated that the cake will use 50,000 tons of flour, which represents 20% of the current supply of flour. The current price of flour is $4000 per ton. Previous study has shown the elasticity of supply, ε_s, for flour to be 0.3 and the elasticity of demand, ε_d to be -1.2.

a. Assuming linear demand curves, what is the percentage change in the price of flour you would anticipate as a result of this project? What do you expect to be the change in quantity supplied as well as the change in quantity demanded by private consumers? What is the opportunity cost of flour that you would use in a cost-benefit analysis of this project?

[Hint: Es = (ΔQs/ΔP)(P/Qs) and Ed =(ΔQd/ΔP)(P/Qd) where Qs is current supply and P is current price.

Note that the amount of flour demanded by the project Qp = ΔQs – ΔQd]

b. Sketch the supply and demand for flour and show the opportunity cost on your sketch.

It is desired to use a rotary vacuum filter to separate slurry containing 20 kg of water per kilogram of solid material. Tests on the rotary filter at the conditions to be used for the filtration have indicated that the dimensionless ratio α/β' is 0.6 and 19 kg of filtrate (not including wash water) is obtained for each 27.8 kg of slurry. The temperature and pressure of the surroundings are 25 oC and 1 atm, respectively. The pressure drop to be maintained by the vacuum pump is 45 kPa. The fraction of the drum area submerged in the slurry is 0.3 and the fraction of the drum area available for suction is 0.1. On the basis of the following assumptions, estimate the kilowatt rating of the motor necessary to operate the vacuum pump if the filter handles 16000 kg/h of slurry. Assumptions are as follows:

Resistance of the filter medium is negligible.

Effects of air leakage are included in the value given for α/β'.

The value of β' is based on the temperature and pressure of the ambient air.

The filter removes all the solids from the slurry.

The vacuum pump operates isentropically with an overall efficiency of 50 percent for the pump and motor.

The ratio of Cp/Cv remains constant at a value of 1.4.

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $20 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $5 million with a 0.2 probability, $1.9 million with a 0.5 probability, and $0.8 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

a) Debt/Capital ratio is 0.
RÔE =
σ =   
CV =

b) Debt/Capital ratio is 10%, interest rate is 9%.
RÔE =
σ =
CV =

c) Debt/Capital ratio is 50%, interest rate is 11%.
RÔE =   
σ =   
CV =

d) Debt/Capital ratio is 60%, interest rate is 14%.
RÔE =   
σ =
CV =

A computer company manufactures 3 types of computers which are personal computers, workbooks and gamebooks. Each personal computer is produced in 0.2 hours, assembled in 0.1 hours, and inspected in 0.05 hours. Each workbook is produced in 0.2 hours, assembled in 0.3 hours, and inspected in 0.075 hours. Each gamebook is produced in 0.4 hours, assembled in 0.4 hours, and inspected in 0.15 hours. At most 600 hours of production, 480 hours of assembly and 160 hours of inspection can be done. The company profits 60$ from a personal computer, 90$ from a workbook, 100$ from a gamebook. Besides, due to the lack of demand, at least 60 personal computer should be ready in the inventory. Formulate an LP that can be used to maximize the profit of computer company. Explain each decision variable, objective function, and constraint with at least one sentence. Write down the standard form and add artificial variables if needed. Find a basic feasible solution to start simplex. Solve the LP by using simplex method step by step. Write down the optimal solution.

Cone of Depression – determini

ng the maximum pumping rate fo

r a specified draw down.

(+20)

A consulting company decides to u

se Pump & Treat to remove the

TCE plume from the aquifer. For an

unconfined aquifer such as this, t

here is a possibility that dr

awdown during the Pump & Treat operation will

lower the water table to the

bottom of the well and that the wa

ter will stop flowing (thi

s is bad). Suppose a 6

inch diameter well is installed

which fully penetrates the 15-m

thick aquifer which has a hydraulic

conductivity of 0.001 m/s. Deter

mine the maximum pumping rate

(in gallons per minute, gpm) that can be

sustained indefinitely if the dr

awdown at an observation well 5

00 m from the pumped well is 12 m and the

drawdown at the pumped well is

limited by the depth of the aqui

fer and the height of the submersible pump,

which you may estimate at 0.3 m

(i.e., drawdown in the pumping

well may not exceed 14.7 m).

Answer: Q = 50.5 gpm.

PLEASE USE R PROGRAMMING LANGUAGE TO ANSWER THESE EXAMPLES. Also please explain any important reasons/tips for how you coded. Thank you!

The Basic Examples:

a) If Statements: Write code that generates a random variable x uniformly between 0 and 1. If x is bigger than 0.6, square it; if x is less than 0.3, set it equal to 5, otherwise set x = 0.

b) Forloops: Write a program that makes a vector of all zeros of length 5.Then write a for loop that fills in this vector with the squares of the integers from 1 to 5. This for loop should iterate over the numbers 1 to 5, square each one, and enter the result in the vector. Show the results in your output/report.

c) Functions: Write a function that takes a number as an input and squares it (so the output is the square of the input number). Rewrite your code from part b) to use your new function, and run the updated code. Do your results match the results you got in part b)?

A wheel alignment shop wants to improve his service by purchasing a new wheel alignment system. He is faced with three outcomes related to the demand on wheel alignment service, and three alternative decisions on alignment system purchase. The table below displays the estimated daily payoffs resulting from all combinations of decisions with outcomes.

Alternative Decisions Outcomes (demand)
O1: High O2: Moderate O3: low
A1: high performance alignment system AED 10,000 AED 5,000 AED -10,000
A2: ordinary alignment system AED 5,000 AED 3,000 AED -5,000
A3: no purchase AED 3,000 AED 2,000 AED 0
Probabilities 0.2 0.5 0.3

1. If the decision is taken under uncertainty, find the best decision using the Maximax criterion. (3.5 Marks)
2. Now with the given outcomes’ probabilities, what is the best decision according to the EMV criterion? (3.5 Marks)
3. Use the EVPI to decide if the shop manager should buy perfect information for AED 2500 or not.

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.5 million with a 0.2 probability, $2.2 million with a 0.5 probability, and $0.4 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations. Debt/Capital ratio is 0. RÔE = % σ = % CV = Debt/Capital ratio is 10%, interest rate is 9%. RÔE = % σ = % CV = Debt/Capital ratio is 50%, interest rate is 11%. RÔE = % σ = % CV = Debt/Capital ratio is 60%, interest rate is 14%. RÔE = % σ = % CV =

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $17 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.9 million with a 0.2 probability, $3.2 million with a 0.5 probability, and $0.5 million with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Debt/Capital ratio is 10%, interest rate is 9%.

Debt/Capital ratio is 50%, interest rate is 11%.

Debt/Capital ratio is 60%, interest rate is 14%.