. Tots Toys makes a plastic tricycle that is composed of three major components:

ID: 445966 • Letter: #

Question

. Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. Current schedules yield the following information. Requirements Component Plastic Time Space Cost to Manufacture Cost to Produce Front 3 10 2 $8 $12 Seat/Frame 4 6 2 6 9 Rear Wheel (each) 0.5 2 0.1 1 3 Available 50,000 160,000 30,000 The company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles so has gathered purchase information for each component. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.

Explanation / Answer

Let

FM = number of fronts made

SM = number of seats made

WM = number of wheels made

FP = number of fronts purchased

SP = number of seats purchased

WP = number of wheels purchased

Min

8FM + 6SM + 1WM + 12FP + 9SP + 3WP

s.t.

3FM + 4SM + .5WM £ 50000

10FM + 6SM + 2WM £ 160000

2FM + 2SM + .1WM £ 30000

FM + FP ³ 12000

SM + SP ³ 12000

WM + WP ³ 24000

FM, SM, WM, FP, SP, WP ³ 0

Let