QuestionKelvin Shoe Stores carries a basic black

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:

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:

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:

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.

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

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