BabyBikes makes plastic tricycles that are constructed with three major parts: a front mechanism (containing the handlebar, front wheel and pedal assembly), a frame unit, and rear wheels. The company has orders for 16,000 of these tricycles. In order to meet this demand, BabyBikes can either manufacture or purchase (or some combination) for each of these components. Below is the following information about this product:

Requirements for Manufacturing

Cost to

Cost to

Component Plastic (in sq ft)

Time (in minutes)

Space (in sq. ft)

Manufacture

Purchase

Front 2

11

3

$9

$13

Seat/Frame 5

7

1

$8

$9

Rear wheel (each) .5

4

.2

$2

$3

Available 38000 sq ft

165,000 minutes

50000 sq ft

The company obviously does not have the resources available to manufacture everything needed for the completion of 16000 tricycles so at least some of the components must be purchased at costs above. 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 16000 fully completed tricycles at the minimum cost.NOTE: Tricycles need 2 rear wheels.

Formulate the linear programming problem only.Be sure to define decision variables (HINT: create a decision variable for Front (Manufacture), Front (Purchase), Seat (Manufacture), Seat (Purchase), etc.), provide objective function, and all constraints.DO NOT SOLVE.