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 that 4,500 pounds of steel are available. What is thenew optimal z-value?

Objective Function Value:
PX:
PY:
PZ:
PW:

What if only 4,400 pounds of steel are available? What is thenew optimal z-value?

Objective Function Value:
PX:
PY:
PZ:
PW:

What is the most that manufacturer should be willing to pay foran additional unit of raw material?

What is the most that manufacturer should be willing to pay foran additional unit of machine hour?

In order to answer the above questions, how many times you didupdate your model and solve it?