Question

Linear Programming Assignment

You must do the necessary calculations in the answer cells. Simply providing a number in the answer cell will not receive any credit.

Problem 1: Use the information below to complete the assignment

van Oploo’s motor cycle company makes two motor cycles. The model "E" has a new engine and a low profile. Model "L" is larger, it uses an older engine and is specifically designed to appeal to women. van Oploo's produces the engines for both models at its facilities in Texas. Each model "E" engine requires 6 hours of manufacturing time and each model "L" engine requires 3 hours of manufacturing time. The manufacturing plant has 1600 hours of engine manufacturing time available for the next production period. The motor cycle frame supplier can provide as many modle "E" frames as needed; however the model "L" supplier can a maximum of 280 model "L" frames for the next production period. Final assembly and testing requires 2 hours of each model "E" and 2.5 hours of each model "L". A maximum of 1000 hours of assembly and testing time are available for the next production period. The company’s accounting department projects a profit contribution of $2400 for each model "E" produced and $2000 for each model "L" produced.

A) Develop a complete linear programming formulation for this problem

B) Using any method from the text or using solver, find the optimal amount of each motor cycle to produce, in order to maximize profits. Be sure to indicate the number of each motor cycle to produce and the total profits that are expected.

Show all of your work below this line -----------------------------------------------------------------------------

Answer 1

A) LP formulation is following:

Let E be the number of new engines and L be the number of old larger engines to be produced.

Max 2400E + 2000L

s.t.

6E+3L <= 1600

L <= 280

2E + 2.5L <= 1000

E, L >= 0

B) Solution using LINGO is following:

Optimal solution:

E = 126.7

L = 280

Optimal profit = $ 864,000