A manufacturing company produces three different types of valves: V412, V512, an

Question

A manufacturing company produces three different types of valves: V412, V512, and V612. It has a firm order from Acme Inc. for 2,000 V412 valves, 3,750 V512 Valves, and 1700 v612 Valves between now nad when the order is due to be delivered, it has 16,500 fabrication hours and 1,600 inspection hours, which aren ot enough to manfufacutre the total quantity ordered. The time required in each department by the various valves is shown in the following table.

Also shown are the costs to manufacture the valves inhouse and the costs to outsource them. For labeling considerations, the company wants to manufacture in-house at least 60% of each type of valve that will be shipped to Acme. How many valves of each type should be made in-house and how many should be outsourced? What will be the total cost to produce acme order?

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valve Fabcrication Hours Inspection Hours In-house cost Outsource Cost v412 2.50 0.25 $17.00 $20.40 v512 3.40 0.30 $19.00 $21.85 v612 3.8 0.45 $23.00 $25.76

Explanation / Answer

Answer:

Step 1: define decision variables

Let xa1 = the number of valve A to produce in­ house

Xa2 = the number of valve A to outsource

Xb1 = the number of valve B to produce in­house

Xb2 = the number of valve B to outsource

Xc1 = the number of valve C to produce in­house

Xc2 = the number of valve C to outsource

Step 2: Objective function.

Minimize cost = 17xa1 + 20.4xa2 + 19xb1 + 21.85xb2 + 23xc1 + 25.76xc2

Step 3: State the constraints:

“Subject to:” Demand:

Valve A: xa1 + xa2 >= 2000

Valve B: xb1 + xb2 >= 3750

Valve C: xc1 + xc2 >= 1700

Resource:

Fabrication: 2.5xa1 + 3.4xb1 + 3.8xc1 <= 16,500

Inspection: .25xa1 + .3xb1 + .45xc1 <= 1,600 60%

In­House requirement

xa1 >= .6(xa1 + xa2) or.4xa1 ­ .6xa2 >= 0

xb1 >= .6(xb1 + xb2) or .4xb1 ­ .6xb2 >= 0

xc1 >= .6(xc1 + xc2) or .4xc1 ­ .6xc2 >= 0

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