A company produces three types of products: P1 , P2 and P3 . Due to limited demands, you are forced to produce no more than a specific quantity of these products. Three types of raw materials: RM1 , RM2 and RM3 are required for the manufacturing process.

The following table summarizes the relevant data. The profits resulting from each unit of P1 , P2 , and P3 are $6, $8, and $10, respectively. The maximum quantities of P1 , P2 , and P3 that the firm can produce are 3,000 units, 2,000 units, and 1,500 units, respectively. The availability of raw materials RM1 , RM2 and RM3 are 18000 units, 30000 units and 36000 units respectively. The per unit cost of RM1 , RM2 , and RM3 is $3, $4, and $2, respectively. The resource requirements for each product can be interpreted as follows:

It takes 2 units of RM1 , 4 units of RM2 , and 5 units of RM3 to produce each unit of P1 .

It takes 4 units of RM1 , 5 units of RM2 , and 6 units of RM3 to produce each unit of P2 .

It takes 5 units of RM1 , 8 units of RM2 , and 10 units of RM3 to produce each unit of P3 .

	P1	P2	P3	Available	Cost per unit
RM1	2	4	5	18000	$3
RM2	4	5	8	30000	$4
RM3	5	6	10	36000	$2
Demand	3000	2000	1500
profit/unit	$ 6	$ 8	$ 10

Formulate this problem as a linear program and obtain the optimal solutions to maximize the total profits under the given constraints.

Answer the following questions:

What is the maximum achievable profit?

How many units of P1 , P2 , and P3 are produced under the optimal plan?

How many units of RM1 , RM2 , and RM3 are used in the optimal plan? 

How much should the company be willing to pay for an additional RM1 unit ? 

How much should the company be willing to pay for an additional unit of RM2 ?

How much should the company be willing to pay for an additional unit of RM3 ?