[لياااان]

. 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 Cost to Cost to
Component Plastic Time Space Manufacture Purchase
Front 3 10 2 8 12
Seat/Frame 4 6 2 6 9
Rear wheel (each) .5 2 .1 1 3
Available 50000 160000 30000

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.

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



ANS:

Min 8FM + 6SM + 1WM + 12FP + 9SP + 3WP
s.t. 3FM + 4SM + .5WM 50000
10FM + 6SM + 2WM 160000
2FM + 2SM + .1WM 30000
FM + FP 12000
SM + SP 12000
WM + WP 24000
FM, SM, WM, FP, SP, WP 0





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