Problem 1.
Nana'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 Nana's Stuffin': (a ,b or c)
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.
d. Design a production plan for Nana's Stuffinusing linear programming and Excel Solver.
|
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
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|
Production rate
|
200 pallets per worker per month
|
|
Hiring cost
|
$5000 per worker
|
|
Firing cost
|
$8000 per worker
|
|
Problem 2
Sparrow 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.
b. Solve this model using the graphical method.
Problem 3
The Mycron Company produces three electrical products-clocks, radios, and toasters. These products have the following resource requirements:
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Resource Requirements
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|
Product
|
Cost/Unit
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Labor Hours/Unit
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|
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.