Suppose we have an Economic Order Quantity (EOQ) problem with discounts.

A (annual demand)= 10000, k (order cost)= 10, c1 (item cost)= 8, h (holding cost)= 0.1

For orders of 2000 or more, the cost is discounted from 8 to 7.3728.

What is the optimal TAC (total annual cost, including order and holding, and also including the purchase costs)?

A 30 kg projectile is launched from the ground at an initial velocity of 300 m/s at an angle of 45 degrees above the horizontal. If air resistance is ignored, determine the following:

a. The projectile's speed at 2000 meters above the ground.

b. The total amount of energy the object has at 3000 m.

c. The maximum height of the projectile.

d. The maximum distance the projectile travels horizontally.

part 1)

Find dy/dx by implicit differentiation.

3x^6+x^5y−2xy^6=8

dy/dx=

part 4)

A campground owner has 2000 meters of fencing. She wants to enclose a rectangular field bordering a lake, with no fencing needed along the lake: see the sketch.

a) Write an expression for the length of the field: 2000-x (this is correct)

b) Find the area of the field (length times width): -x^2+2000x (this is correct)

c) Find the value of x leading to the maximum area:

d) Find the maximum area:

I got (2y^6-5yx^4-30x^5)/(x^5-12xy^5)

part 2)

sqrt (x+y)=9+x^2y^2

dy/dx= (80+4x^3y^4+36xy^2)/(1-4x^4y^3-36x^2y)

part 3)

Use implicit differentiation to find an equation of the tangent line to the curve

sin(x+y)=6x−6y at the point (π,π).

Tangent Line Equation: y= (5x/7)-(2pi/7)

Consider the following given information, determine the 3-year moving averages that would have been used to forecast the sales (in millions) for the years subsequent to each group of three years. Determine the forecast error associated with each forecast.

Year(t) 1993／ 1994 ／1995 ／1996 ／1997 ／1998 ／1999 ／2000

Profit Y(t) 0.9 ／ 1.1 ／1.2 ／ 1.3 ／ 1.4 ／ 1.5 ／ 1.6 ／ 1.7

You may create a table with below information.

Year ／ Sales in millions ／ 3-year Moving Forecast ／ Forecast error ／ Absolute error

b) In the below table, by using the actual level of sales for 1994 of 1.1 million dollars as the “seed” forecast for 1995, determine the forecast for each annual sales amount by the method of simple exponential smoothing. First use a smoothing constant of alpha = 0.8, then use a smoothing constant of alpha = 0.2, and compare the two sets of forecasts.

Year(t) 1993 /1994 /1995 /1996 /1997 /1998 /1999 /2000

Sales in millions Y(t) 0.9 /1.1 /1.5 /1.3 /1.1 /1.7 /1.9 /2.3

Glucose (C6H12O6) is the primary source of metabolic energy for vertebrates.

a)Determine the amount of available glucose in 500g of sucrose

b)Write a balanced chemical reaction for the combustion of glucose. The products of the combustion are carbon dioxide and liquid water.

c)Using tabulated Gfo values, calculate the free energy of reaction for the combustion of glucose.

d)A normal human body requires approximately 2000 kJ of energy to sustain itself. Assuming that glucose is the primary source of metabolic energy, how many grams of glucose must be consumed in order to provide 2000 kJ of energy?

e)The metabolism of glucose in vertebrate systems requires a number of steps, which when added together result in the reaction from part (a). Explain why it is possible to calculate the metabolic energy even though there is more than one step in the process.

Write reactions that correspond to the following changes.

a)Gof for solid Aluminum oxide

b) the standard free energy of combustion of liquid ethanol, C2H5OH(l).

c)the standard enthalpy of neutralization of barium hydroxide solution by aqueous hydrochloric acid.

d) aqueous HCl

Assignment6: Hypothesis testing

Exercise1 Acomponent’s mean life is supposed to be1000 hours, now we randomly select 25 components out of 2000 components and obtain a mean life of 950 hours, prior study shows that these 2000 components follow a normal distribution with standard deviation of 100 hours.

1.Construct your hypothesis testing ,is this a two -tailed test or a none-tailed test?

2.Conduct your hypothesis testing under the confidence level of 5%, using both classical and P-value approach.

3.State your conclusion.

Exercise2 The mean proportion of water in a one solvent is supposed to be 0.5%, now we take a random sample and test out that in the sample the mean proportion of water is 0.4525 and its standard deviation is 0.035%.

1.Construct your hypothesis testing, is this a two-tailed test or a none-tailed test?

2.Conduct your hypothesis testing under the confidence level of 5%,using both classical and P-value approach.

3.State your conclusion.

The following is an excerpt from an unadjusted trial balance of Bob's BBQ Company:
DB CR      

Accounts Receivable                   12000

Notes Receivable, trade               2000

Allowance for Doubtful Accounts 200

Sales Revenue 1040000

Returned Sales 3000

Purchases 50000

Purchase Returns and Allowances 2000

Retained Earnings 15700

Required

Prepare the appropriate entries indicated below. Each item is independent.
a) Record bad debt expense, assuming company experience indicates that 40 percent of sales are on account and 2 percent of net credit sales prove uncollectible.
b) Record bad debt expense if an aging schedule indicates that $1,000 of the receivable at the end of this year will not be collected.
c) Record bad debt expense if company policy requires the allowance for doubtful accounts be maintained at 5 percent of total trade receivables.
d) In April, four accounts totalling $500 were in excess of 90 days old and were determined by the collection department to be uncollectible.
e) In May of the year, one of the accounts written off in (d) was paid in full in the amount of $200.

12/31/17 Co estimates 4% of its outstanding $300,000 in receivables will be uncollectable. ADA already has a credit balance of $1000.

1. Make the JE to record estimated uncollectable receivables.

2. On 1/31/18 $2000 of receivables is determined to be uncollectable. Make JE.

3. What is ADA balance 2/1/18?

4. What are net (or cash) receivables on 2/1/18?

5. Are the two net receivable figures, from both before and after 1/31 write off different in value? Why or why not?

6. On 2/3/18 Co learns the $2000 it had written off is now paid in full.

7. 2/15/18 Co sells $100,000 of receivables to Factor Co at a 5% service charge.

8. 3/3/18 Co sells $1000 of goods to customer who paid with Visa or Mastercard where the card company charges 5% fee.

1. Co accepts a $10,000 Note in settlement from a customer who already owes Co $10,000.

Please answer all parts thank you.

You are the manager of a project to improve the billing process at your firm. The table below contains the data you will need to conduct a cost analysis of the project. Indirect costs are $1600 per week, and penalty costs are $1200 per week after week 12.

a- What is the minimum-cost schedule for this project?

b- What is the difference in total project costs between the earliest completion time of the project using "normal" times and the minimum-cost schedule you derived in part a. Please show work in POM QM as well as outlining the answer.