Formulate and solve a linear programming model for this


Problem S14

Mama's Stuffin' is a popular food item during the fall and winter months, but it is marginal in the spring and summer. Use the following demand forecasts and costs to determine which of the following production planning strategies is best for Mama's Stuffin': 

a. Level production over the 12 months.

b. Produce to meet demand each month. Absorb variations in demand by changing the size of the workforce.

c. Keep the workforce at its current level. Supplement with overtime and subcontracting as necessary.

 

Month

Demand Forecast

March

2000

April

1000

May

1000

June

1000

July

1000

August

1500

September

2500

October

3000

November

9000

December

7000

January

4000

February

3000

 

Overtime capacity per month

Regular production

Subcontracting capacity per month

Unlimited

Regular production cost

$30 per pallet

Overtime production cost

$40 per pallet

Subcontracting cost

$50 per pallet

Holding cost

$2 per pallet

Beginning workforce

10 workers

Production rate

200 pallets per worker per month

Hiring cost

$5000 per worker

Firing cost

$8000 per worker

Problem S14.1.

Barrows Textile Mills produces two types of cotton cloth-denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of cotton and 3000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit.

a.      Formulate and solve a linear programming model for this problem.

Solve this model using the graphical method.

Problem S14-2.

The Tycron Company produces three electrical products-clocks, radios, and toasters. These products have the following resource requirements:

 

Resource Requirements

Product

Cost/Unit

Labor Hours/Unit

Clock

$ 7

2

Radio

 10

3

Toaster

  5

2

The manufacturer has a daily production budget of $2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios, for $20, and toasters, for $12. The company desires to know the optimal product mix that will maximize profit.

Formulate and solve a linear programming model for this problem.

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