A company manufactures 3 products: P1, P2 and P3. Each product requires raw materials, manpower and machine time. The machine used by the company has just suffered a fatal failure and the company is looking to replace it. It has the choice between 2 machines, M1 and M2. The following table presents relevant information on the raw materials, labour and machine time required to manufacture the products.

Product	Commodities (in kg/unit)	Labor (in h/unit)	Machine time M1 (in h/unit)	Machine time M2 (in h/unit)
P1 P2 P3	4 2 1	2 0.5 3	2 1 4	1 3 5
Availability (per month)	1000 kg	500 hours	350 hours	400 hours

The cost of use is $900/month and $1,000/month for the M1 and M2 machines respectively. The unit profits are independent of the machine used and are $8, $4 and $6 respectively for P1, P2 and P3 products.

To maximize its profits, the company uses the following linear model: X1 - number of units of the P1 product to be manufactured

X2 - number of units of the P2 product to be manufactured

X3 - number of units of the P3 product to be manufactured

X11 - number of units of the P1 product to be manufactured if you buy the M1 X12 machine - number of units of the P1 product to be manufactured if you buy the M2 X21 machine - the number of units of the P2 product to be manufactured if you buy the M1 X machine22 - number of units of the P2 product to be manufactured ifthe M2 X31 machine isprocured - number of units of the P3 product to be manufactured if you buy the M1 X32 machine - the number of units of the P3 product to be manufactured if you buy the M2 machine

Y1 - 1 if you buy the machine M1, 0 if not Y2 - 1 if you buy the machine M2, 0 if not

Goal:

MAX Z - 8X1 - 4X2 - 6X3 - 900Y1 - 1000Y2

Constraints:

X1 - X11 - X12 - 0 X2 - X21 - X22 - 0 X3 - X31 - X32 - 0

4X1 - 2X2 - X3 1000

2X1 - 0.5X2 - 3X3 500

2X11 - X21 - 4X31 - 350Y1 0 X12 - 3X22 - 5X32 - 400Y2 0

X1, X2, X3, X11, X12, X21, X22, X31, X32 0 and all

Solve using the technology tool SOLVER EXCEL

1. What machine should we buy? How many units of each product should be manufactured? What is the maximum profit?

The following questions are independent of each other and refer to the original model. For each of the following situations,indicate the optimal solution (machine to be procured, number of units of each product to be manufactured, maximum profit).

2. It was decided to increase the selling price of the P2 product by $2.
3. The available raw materials are 1200 units per month.
4. Following an employee's retirement, the workforce time of the P2 product doubles.
5. A new M3 machine would be available. Its cost of use would be $500 per month. The machine times required to manufacture the products would be 3, 2 and 2 hours respectively for P1, P2 and P3 products respectively. The availability of this machine would be 600 hours/month.