A manufacturer produces three models (1,2,3) of a certain product. He uses two t

Question

A manufacturer produces three models (1,2,3) of a certain product. He uses two types of raw material (1 and 2) of which 4000 and 6000 units are available,respectively. The raw material requirements per unit of three models are given below

A market survey indicates there is demand for 200,300, and 150 units, respectively, of Models 1,2 and 3. However, management has dictated that the quantity of Model 3 produced must be atleast 3 times the quantity of Model 2 produced. Assume the profit per unit of Models 1,2 and 3 are $30,20 and 50.

a) Formulate a LP to determine the number of units of each product which will maximize profit. (write decision variables and constraint, no need to solve)

b)Suppose at most 350 additional units of raw material 1 can be purchased at a rate of $5/unit. Repeat part a), this time accounting for the possibility of purchasing additional resources. (No need to re-define any varibales that were defined in part a.)

c)The manufacturer is considering investing in a marketing campaign that will increase the demand for Models 1 and 3. Suppose that each investment of $50 increases the demand for Models 1 and 3 by one unit each. Repeat part a), this time taking into account the possibility of investing in marketing. (Note: This problem should be considered independently of part b)

Explanation / Answer

a. The decision variables for the given problem will be:

X1 = Number of Model 1 produced

X2 = Number of Model 2 produced

X3 = Number of Model 3 produced

Subject to the constraints:

And thus the objective function is:

Maximize Z = (30*X1)+(20*X2)+(50*X3)

For b:

For part c:

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