A linear programming computer package is needed.

The Silver Star Bicycle Company will be manufacturing both men's and women's models for its Easy-Pedal 10-speed bicycles during the next two months. Management wants to develop a production schedule indicating how many bicycles of each model should be produced in each month. Current demand forecasts call for 150 men's and 125 women's models to be shipped during the first month and 200 men's and 150 women's models to be shipped during the second month. Additional data are shown.

Model	Production Costs	Labor Requirements (hours)		Current Inventory
		Manufacturing	Assembly
Men's	$120	2.0	1.5	20
Women's	$90	1.6	1.0	30

Last month the company used a total of 1,000 hours of labor. The company's labor relations policy will not allow the combined total hours of labor (manufacturing plus assembly) to increase or decrease by more than 100 hours from month to month. In addition, the company charges monthly inventory at the rate of 2% of the production cost based on the inventory levels at the end of the month. The company would like to have at least 25 units of each model in inventory at the end of the two months. Only integer amounts of bicycles can be produced.

(a)

Establish a production schedule that minimizes production and inventory costs and satisfies the labor-smoothing, demand, and inventory requirements.

men's model in month 1

bicycles women's model in month 1

bicycles men's model in month 2

bicycles women's model in month 2

bicycles Total Cost $

What inventories will be maintained?

Inventory Schedulemen's model in month 1

bicycles women's model in month 1

bicycles men's model in month 2

bicycles women's model in month 2

bicycles

What are the monthly labor requirements?

previous month hrs month 1 hrs month 2 hrs

(b)

If the company changed the constraints so that monthly labor increases and decreases could not exceed 50 hours, what would happen to the production schedule?

men's model in month 1

bicycles women's model in month 1

bicycles men's model in month 2

bicycles women's model in month 2

bicycles Total Cost $

How much will the cost increase?

$

2.)

A linear programming computer package is needed.

Greenville Cabinets received a contract to produce cabinets for a major furniture distributor. The contract calls for the production of 3,300 small cabinets and 4,100 large over the next two months, with the following delivery schedule

Model	Month 1	Month 2
Small	2,100	1,200
Large	1,500	2,600

Greenville estimates that the production time for each small cabinet is 0.7 hours and the production time for each large cabinet is 1 hour. The raw material costs are $10 for each small cabinet and $12 for each large cabinet. Labor costs are $22 per hour using regular production time and $33 using overtime. Greenville has up to 2,400 hours of regular production time available each month and up to 1,000 additional hours of overtime available each month. If production for either cabinet exceeds demand in month 1, the cabinets can be stored at a cost of $5 per cabinet. For each product, determine the number of units that should be manufactured each month on regular time and on overtime to minimize total production and storage costs. (Round your answers to the nearest integer. Let SaR = regular small cabinets for month 1, SbR = regular small cabinets for month 2, LaR = regular large cabinets for month 1, LbR = regular large cabinets for month 2, SaO = overtime small cabinets for month 1, SbO = overtime small cabinets for month 2, LaO = overtime large cabinets for month 1, and LbO = overtime large cabinets for month 2)

(SaR, SbR, LaR, LbR, SaO, SbO, LaO, LbO)=

Total Production Cost = $