Quiz 4

A manufacturer makes and sales four types of products:  Product X, Product Y, Product Z, and Product W.  

The resources needed to produce one unit of each product and the sales prices are given in the following Table.

• Currently, 4,600 pounds of steel and 5,000 machine hours are available.

• To meet customer demands, exactly 950 total products must be produced.

• Customers also demand that at least 400 units of Product W be produced.

Formulate an LP that can be used to maximize sales revenue for the manufacturer.

LP Formula

Let Pi be the number of product type i produced by the manufacturer, where i = X, Y, X, and W.

MAXIMIZE  4 PX + 6 PY + 7 PZ + 8 PW

Subject To

2 PX + 3 PY + 4 PZ + 7 PW <= 4600   ! Available Steel

3 PX + 4 PY + 5 PZ + 6 PW <= 5000   ! Available Machine Hours

PX + PY + PZ + PW    = 950               ! Total Demand

                            PW >= 400               ! Product W Demand

PX >=0

PY >=0

PZ >=0

PW >=0

Suppose manufacturer raises the price of Product Y by 50¢ per unit. What is the new optimal solution to the LP?

 Strong Tool Company has been considering purchasing a new lathe to replace a fully depreciated lathe that would otherwise last 5 more years. The new lathe is expected to have a​ 5-year life and depreciation charges of $2,060i n Year​ 1; $3,296 in Year​ 2; $1,957 in Year​ 3; $1,236 in both Year 4 and Year​ 5; and $515 in Year 6. The firm estimates the revenues and expenses​ (excluding depreciation and​ interest) for the new and the old lathes to be as shown in the following table

. The firm is subject to a 40% tax rate on ordinary income.

a. Calculate the operating cash inflows associated with each lathe.​ (Note: Be sure to consider the depreciation in year​ 6.)

b. Calculate the operating cash inflows resulting from the proposed lathe replacement.

c. Depict on a time line the incremental operating cash inflows calculated in part b.

A statistical program is recommended.

The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

(a) Use α = 0.01 to test the hypotheses

for the model y = β₀ + β₁x₁ + β₂x₂ + ε,  where

Find the value of the test statistic. (Round your answer to two decimal places.)

Use α = 0.05 to test the significance of β₁.

Find the value of the test statistic. (Round your answer to two decimal places.)

Use α = 0.05 to test the significance of β₂.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

Catena's Marketing Company has the following adjusted trial balance at the end of the current year. Cash dividends of $620 were declared at the end of the year, and 580 additional shares of common stock ($0.10 par value per share) were issued at the end of the year for $2,320 in cash (for a total at the end of the year of 850 shares). These effects are included below: Catena’s Marketing Company Adjusted Trial Balance End of the Current Year Debit Credit Cash $ 1,590 Accounts receivable 2,310 Interest receivable 270 Prepaid insurance 1,750 Long-term notes receivable 2,930 Equipment 15,900 Accumulated depreciation $ 2,810 Accounts payable 2,200 Dividends payable 620 Accrued expenses payable 3,910 Income taxes payable 2,530 Unearned rent revenue 400 Common Stock (850 shares) 85 Additional paid-in capital 3,475 Retained earnings 5,070 Sales revenue 36,750 Interest revenue 120 Rent revenue 580 Wages expense 18,300 Depreciation expense 1,740 Utilities expense 360 Insurance expense 720 Rent expense 9,900 Income tax expense 2,780 Total $ 58,550 $ 58,550 Prepare a statement of stockholders' equity for the current year. (Reductions in account balances should be indicated with a minus sign.)

Romney's Marketing Company has the following adjusted trial balance at the end of the current year. No dividends were declared. However, 500 shares ($0.10 par value per share) issued at the end of the year for $3,000 are included below:

a. Compute total assets for Romney’s Marketing Company based on the adjusted trial balance.

b. Compute the company's total asset turnover for the current year, assuming total assets at the end of the prior year were $16,050.

Color Paint Shop, Inc. is an accrual basis taxpayer that paints automobiles. During 2018, the company painted Sam’s car and was to receive $1,000 payment from his insurance company. Sam was not satisfied with the work, however, and the insurance company refused to pay. In December 2018, Color and Sam agreed that Color would receive $800 for the work, subject to final approval by the insurance company. In the past, Color had come to terms with customers only to have the insurance company negotiate an even smaller amount. In May 2019, the insurance company reviewed the claim and paid the $800 to Color. An IRS agent thinks that Color should report $1,000 of income in 2018 and deduct a $200 loss in 2019.

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the delivery cycle time for each month.

1-c. Compute the manufacturing cycle efficiency (MCE) for each month.

2. Evaluate the company’s performance over the last four months.

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE.

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE.

DataSpan, Inc., automated its plant at the start of the current year and installed a flexible manufacturing system. The company is also evaluating its suppliers and moving toward Lean Production. Many adjustment problems have been encountered, including problems relating to performance measurement. After much study, the company has decided to use the performance measures below, and it has gathered data relating to these measures for the first four months of operations.

Management has asked for your help in computing throughput time, delivery cycle time, and MCE. The following average times have been logged over the last four months:

Required:

1-a. Compute the throughput time for each month.

1-b. Compute the delivery cycle time for each month.

1-c. Compute the manufacturing cycle efficiency (MCE) for each month.

2. Evaluate the company’s performance over the last four months.

3-a. Refer to the move time, process time, and so forth, given for month 4. Assume that in month 5 the move time, process time, and so forth, are the same as in month 4, except that through the use of Lean Production the company is able to completely eliminate the queue time during production. Compute the new throughput time and MCE.

3-b. Refer to the move time, process time, and so forth, given for month 4. Assume in month 6 that the move time, process time, and so forth, are again the same as in month 4, except that the company is able to completely eliminate both the queue time during production and the inspection time. Compute the new throughput time and MCE.