OSCORP Industries Inc makes three components for sale to rob

OSCORP Industries, Inc. makes three components for sale to robot manufacturers. The components are processed on two machines: a sharper and a grinder. The times (in minutes) required in each machine are as follows:

Component 1 (C1)

Component 2(C2)

Component 3(C3)

Shaper

6

4

4

Grinder

4

5

2

The shaper is available for 7200 minutes, and the grinder available for 6600 minutes. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6 and $9, respectively.

Develop a mathematical linear programming model.

Use excel to solve for the maximum profit. How many do you need to produce from each component in order to maximize your profit?

Run the sensitivity analysis report in excel to answer the following questions:

If more time could be available on the grinder, how much would it be worth?

If your managers says we need to reduce the capacity of shaper to 6200 minutes, what would be the impact of this reduction on your profit?

Since more units of component 3 can be sold by reducing the price by $4, should the company reduce the price?

Solution

Let c1 the no.of units of component 1 produced
c2 the no.of units of component 2 produced
c3 the no.of units of component 3 produced
maximum $8c1+$6c2+$9c3   
subject to
1. 6c1+4c2+4c3(=7200 sharper time available(in minutes)
2. 4c1+5c2+2c+(=6600 grinder time available(in min)
3. c3(=200 maximum #of units of component 3
4. c1 (=1000 maximum #of units of component 1
5. c2 (=1000 maximum #of units of component 2
6. c1 (=600 minimum #of units of component 1
7.c1, c2, c3 )= 0 non megativity

Nothing, 300 minutes of slack time on the grinder at the optimal solution.

NO,it is not profitable for the company by reducing the price by $4.