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# QM 670 Exam II

Question # 00006159
Subject: General Questions
Due on: 01/29/2014
Posted On: 01/05/2014 05:16 PM

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1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of \$30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:

 Order Quantity Price/pair 0-99 \$36 100-199 32 200-299 30 300+ 28

For a price of \$36, the optimal order quantity is ___________. (4)

2. Redo #1 if they allow backordered items with a shortage cost of \$4/quarter.

Optimal order quantity = ___________. (4)

1. Kelvin Shoe Stores carries a basic black dress shoe for men that sells at a rate of 500 each quarter. Their current policy is to order 500 per quarter, with a fixed cost of \$30/order. The annual holding cost is 20% of the cost of items held. The following cost structure is applicable:

 Order Quantity Price/pair 0-99 \$36 100-199 32 200-299 30 300+ 28

The optimal order quantity is ______________. (5)

4. The Employee Credit Union at Directional State University is planning the allocation of funds for the coming year. ECU makes four types of loans and has three additional investment instruments. Each loan/investment has a corresponding risk and liquidity factor (on a scale of 0-100, with 100 being the most risky/liquid). The various revenue-producing instruments are summarized in the table below:

 Instrument Annual Rate of Return (%) Risk Factor Liquidity Factor Automobile loans 8 50 0 Furniture loans 10 60 0 Other secured loans 11 70 0 Unsecured loans 14 80 0 Risk-free securities 5 0 100 Corporate stock fund 9 60 90 Corporate bond fund 8 50 80

ECU has \$2,000,000 available for investment during the coming year. However, state laws and pesky stakeholders impose certain restrictions on choice of investment instruments. Risk-free securities may not exceed 30% of total funds available for investment. Unsecured loans may not exceed 10% of total funds invested in loans. The funds invested in automobile loans must not be less than the total of funds invested in furniture and other secured loans. The average risk factor may not exceed 60, and the average liquidity factor must be at least 40. Formulate a linear program for ECU. DO NOT SOLVE THE LP. (10)

5. Powers Tire Company (which specializes in tires for vehicles ca. 1965) needs your expertise to help them schedule over the next three months. They can make tires using regular labor, overtime labor, or subcontracting. Their capacities (in tires) are as follows: 700/month for regular labor, 50/mo. for overtime labor, and 150/mo. for subcontracted labor in March and April, and 130/mo. for subcontracted labor for May. It costs \$40/tire to produce with regular labor, \$50/tire with overtime, and \$70/tire with subcontracting. It costs \$2/tire/month to carry a tire in inventory. Tires can be produced only for the current or future periods, e.g., tires cannot be produced in May to fill demand in April. Demands for the next three periods are 800, 1000, and 750, for March, April, and May, respectively, and all demand must be met. Check (or shade) all that apply. (12)

1. This is an integer program.

1. This is a transportation problem.

1. The cost of using regular labor in April to fill March demand is \$40/tire.

1. The cost of using overtime labor in April to fill May demand is \$52/tire.

1. We would need at least one dummy row.

1. We would need at least one dummy column.

6. Hungry Birds, Inc. manufactures birdseed. One variety consists of wheat. They are trying to determine the optimal mix of buckwheat (X1), sunflower (X2), and poppy (X3) (each in lbs.). Relevant information is provided in the following table. In addition, the final mix is required to contain at least 500 lbs. of poppy. Also, the total weight of the buckwheat may not exceed the total weight of the sunflower in the final mix.

 Nutritional Item Proportional Content Total Requirement Buckwheat Sunflower Poppy Fat 0.04 0.06 0.05 480 Protein 0.12 0.10 0.10 1200 Roughage 0.10 0.15 0.07 1500 Cost/lb. \$0.18 \$0.10 \$0.11

The output of the linear program is given on the following page.

LINEAR PROGRAMMING PROBLEM

MIN 0.18X1+0.1X2+0.11X3

S.T.

1) .04X1+.06X2+.05X3>480

2) .12X1+.1X2+.1X3>1200

3) .1X1+.15X2+.07X3<1500

4) 1X3>500

5) 1X1-1X2<0

OPTIMAL SOLUTION

Objective Function Value = 1237.500

Variable Value Reduced Costs

-------------- --------------- ------------------

X1 0.000 0.050

X2 8250.000 0.000

X3 3750.000 0.000

Constraint Slack/Surplus Dual Prices

-------------- --------------- ------------------

1 202.500 0.000

2 0.000 -1.188

3 0.000 0.125

4 3250.000 0.000

5 8250.000 0.000

OBJECTIVE COEFFICIENT RANGES

Variable Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

X1 0.130 0.180 No Upper Limit

X2 No Lower Limit 0.100 0.110

X3 0.100 0.110 0.160

RIGHT HAND SIDE RANGES

Constraint Lower Limit Current Value Upper Limit

------------ --------------- --------------- ---------------

1 No Lower Limit 480.000 682.500

2 1026.667 1200.000 2142.857

3 840.000 1500.000 1760.000

4 No Lower Limit 500.000 3750.000

5 -8250.000 0.000 No Upper Limit

(15)

a. If this had been run as an integer program, we would obtain a different solution. (Check/shade if true.)

b. If we could reduce the fat requirement by 100 lbs., the optimal solution would change. (Check/shade if true.)

c. A new customer wants a mix with at least 20% buckwheat. Would this change the optimal solution? If so, would it increase or decrease? Check/shade the following:

Change?

Increase?

d. Nora in Accounting noted a glitch in her software, and stated that the cost estimates should be changed. She said the cost values should be \$0.17 for buckwheat, \$0.12 for sunflower, and \$0.12 for poppy. Would this be a cause for concern? If so, which component(s) would be affected? Check/shade the following:

We should be concerned.

Buckwheat?

Sunflower?

Poppy?

e. If you could relax the requirement on one nutritional item, which would be the best choice to achieve the lowest cost? Fill in the blank.

________________________

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#### QM 670 Exam II

Tutorial # 00005918
Posted On: 01/05/2014 05:17 PM
Posted By:
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QM_670_Exam_II.docx (19.97 KB)
Preview: 500 xxx quarter, xxxx a fixed xxxx of \$30/order xxx annual xxxxxxx xxxx is xxx of the xxxx of items xxxx The xxxxxxxxx xxxx structure xx applicable:Order QuantityPrice/pair0-99\$36100-19932200-29930300+28For x price of xxxx the xxxxxxx xxxxx quantity xx ___________ (4)SolutionEOQ x sqrt(2*D*S/H) = xxxx (2*(500*4)*30/(0 xxxxxx x 129 xx = 129 xxxxxxxx for \$36, xxxx 0-99 xxx xx ordered xxx EOQ is xxxxxxxxxx at this xxxx structureRedo xx xx they xxxxx backordered items xxxx a shortage xxxx of xxxxxxxxxx xxxxxxx order xxxxxxxx = ___________ xxxxxxxxxxxxx backordered items xxxx shortage xxxx xx \$4/quarter xxx there, optimal xxxxxxxx will not xxxxxxxxxxxx Shoe xxxxxx xxxxxxx a xxxxx black dress xxxx for men xxxx sells xx x rate xx 500 each xxxxxxx Their current xxxxxx is xx xxxxx 500 xxx quarter, with x fixed cost xx \$30/order xxx xxxxxx holding xxxx is 20% xx the cost xx items xxxx xxx following xxxx structure is xxxxxxxxxxxxxxxx QuantityPrice/pair0-99\$36100-19932200-29930300+28The optimal xxxxx quantity xx xxxxxxxxxxxxxx (5)SolutionFor xxxxxx = sqrt xxxxxxxxxxxxxxxx 2*36)) = xxx 09 x xxx unitsAs, xxx \$36, only xxxx can be xxxxxxxx so xxxx xx not xxxxxxxxxx \$32EOQ = xxxx (2*(500*4)*30/(0 2*32)) x 136 xx x 137 xxxxxxxx \$30EOQ = xxxx (2*(500*4)*30/(0 2*30)) x 141 xx x 142 xxxxxxxx for \$30, xxxx 200-299 can xx ordered, xx xxxx is xxx optimalFor \$28EOQ x sqrt (2*(500*4)*30/(0 xxxxxx = xxx xxx 147 xxxxxxxx for \$30, xxxx >300 can xx.....
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