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Quiz 4 A manufacturer makes and sales four types of products:  Product X, Product Y, Product Z, and...

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Advance Math

Quiz 4

A manufacturer makes and sales four types ofproducts:  Product X, Product Y, Product Z, and ProductW.  

The resources needed to produce one unit of each product and thesales prices are given in the following Table.

Resource

Product X

Product Y

Product Z

Product W

Steel (lbs)

2

3

4

7

Hours of Machine Time (hours)

3

4

5

6

Sales Price ($)

4

6

7

8

  • Currently, 4,600 pounds of steel and 5,000 machine hours areavailable.
  • To meet customer demands, exactly 950 total products must beproduced.
  • Customers also demand that at least 400 units of Product W beproduced.

Formulate an LP that can be used to maximize sales revenue forthe manufacturer.

LP Formula

Let Pi be the number of product type i produced by themanufacturer, where i = X, Y, X, and W.

MAXIMIZE  4 PX + 6 PY + 7 PZ + 8 PW

Subject To

2 PX + 3 PY + 4 PZ + 7 PW <= 4600   !Available Steel

3 PX + 4 PY + 5 PZ + 6 PW <= 5000   !Available Machine Hours

PX + PY + PZ + PW    =950               !Total Demand

                            PW>=400               !Product W Demand

PX >=0

PY >=0

PZ >=0

PW >=0

Suppose the sales price of Product Z is decreased by 60¢. Whatis the new optimal solution to the LP?

Objective Function Value:

PX:

PY:

PZ:

PW:

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The following information is available for a company: \table[[Beginning inventory,$35,000