Question

Tots Toys: Introduction The new three questions refer to the following information: 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. Please note that each tricycle requires two rear wheels, the front wheel is included in the front wheel-pedal assembly. The company has orders for 15,000 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.

Answer 1

Answer:

Using slover in excel, the optimum cost will be $230,000

Explanation:

et ‘a’ be the number of fronts made.

Let ‘b’ be the number of seats made.

Let ‘c’ be the number of wheels made.

Let ‘x’ be the number of fronts purchased.

Let ‘y’ be the number of seats purchased.

Let ‘z’ be the number of wheels purchased.

Minimum cost (z) = 8a + 6b +1c + 12x + 9y + 3z

3a + 4b + 0.5c <= 50000

10a + 6b + 2c <= 160000

2a + 2b + 0.1 <= 30000

a + c >= 120000

b +y >= 120,000

c + z > =24000

a, b, c, x, y, z >= 0