Question

A manufacturing company has a pool of 50 labor hours. A customer has requested two products, Product A and Product B, and has requested 15 and 20 of each respectively. It requires 2 hours of labor to produce Product A and 3 hours of labor to produce Product B. The company can obtain up to 50 additional hours of labor if required. In-house labor costs $25 per hour while contracted labor costs $45 per hour.

Draw the network flow model that captures this problem.

Write out the LP formulation for this problem.

Solve this system – the network flow problem. [Provide a screen shot of your Solver solution and/or any Solver Reports you deem necessary.]

What is the company’s labor plan to develop the products, A and B, to fulfill the customer’s order? And, what is the associated cost to the company?

Answer 1

1) Network flow model is following

2) LP formulation is as follows

Let HA and HB be the number of inhouse labor hours used to produce products A and B respectively

and CA and CB be the number of contracted labor hours used to produce products A and B respectively

Min (HA+HB)*25 + (CA+CB)*45

s.t.

HA+HB <= 50

CA+CB <= 50

HA/2 + CA/2 = 15

HB/3 + CB/3 = 20

HA, HB, CA, CB >= 0

3) Solution of the model using Solver is as follows

Formula:

F2 =SUMPRODUCT(B2:E2,$B$8:$E$8)   copy to F2:F6

Solver Answer report is following

4)

Company's labor plan is such that 50 inhouse labor hours should be used for producing B and 30 and 10 contracted labor hours should be used for production of A and B respectively.

Associated cost to the company = $ 3050