Question

# A manufacturing company has a pool of 50 labor hours. A customer has requested two products,...

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?

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

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

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