Instructions: Answer each question. Use Lindo to solve all problems. Show all wo
ID: 3865977 • Letter: I
Question
Instructions: Answer each question. Use Lindo to solve all problems. Show all work by describing variables, stating assumptions, illustrating model and showing output solution to the problem.
1. Tots Toys (10 Points)
Tots toys makes a kids plastic bicycle that is composed of three major components: a front assembly, a seat/frame unit and a front and rear wheel assembly. The company has orders for 12,000 bikes. Current schedules yield the following information regarding the manufacturing and/or buying requirements:
Manufacturing Resources
Component
Plastics (lbs)
Time (hours)
Space (Sq. Ft.)
Cost to Manufacture
Cost to Purchase
Front Assembly
3
10
2
$8
$12
Seat/Frame
4
6
2
$6
$9
Front & Rear Wheels
0.5
2
0.1
$1
$3
Amount Available
50,000
16,000
30,000
In the assembly of one bike, (1) front assembly, (1) seat/frame and (2) wheels (one for front and one for back) are used. The company obviously does not have the resources available to manufacture everything needed for the completion of 12,000 bikes and has the option to purchase the components from an outside supplier. Develop a linear programming model to determine how many of each component should be manufactured and purchased to provide 12,000 completed bikes at the minimum cost.
(Optimal Cost Value from Lindo)
Manufacturing Resources
Component
Plastics (lbs)
Time (hours)
Space (Sq. Ft.)
Cost to Manufacture
Cost to Purchase
Front Assembly
3
10
2
$8
$12
Seat/Frame
4
6
2
$6
$9
Front & Rear Wheels
0.5
2
0.1
$1
$3
Amount Available
50,000
16,000
30,000
Explanation / Answer
Min 8FM + 6SM + 1WM + 12FP + 9SP + 3WP
s.t. 3FM + 4SM + .5WM <= 50000
10FM + 6SM + 2WM <= 160000
2FM + 2SM + .1WM <= 30000
FRONT + FRONTS_PURCHASED >= 12000
SEATS + SEATS_PURCHASED >= 12000
WHEELS + WHELLS_PURCHASED >= 24000
FRONT, SEATS, WHEELS, FRONTS_PURCHASED, SEATS_PURCHASED, WHELLS_PURCHASED >= 0