Reference no: EM13711042

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.