Question

Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours for each unit produced. Assume total production capacity remains 40. Use y as the number of product 2 produced.
a.) Show the mathematical model when both products are considered simultaneously.
b.) Identify the controllable and uncontrollable inputs for this model.
c.) Draw the flowchart of the input-output process for this model
d.) What are the optimal solution values of x and y?
e.) Is the model developed a deterministic or a stochastic model? Explain.

Answer 1

Answer:

Answer is explained below in the explanation section.

Explanation:      

a) Mathematical Model:

Data Given:

Unit Profit = $5 for product 2

Unit Profit = $10 for product 2

Time = 5 hours for product 1 each unit

Time = 2 hours for product 2 each unit

Production Capacity = 40 units

y = number of product 2 produced.

x = number of product 1 produced.

Profitability from product 1 = $10/5hours

Profitability from product 1  = $2

Profitability from product 2 = $5/2 hours

Profitability from product 2 = $2.5

Profitability from product 2 > Profitability from product 1

Max 10x + 5y subject to constraints.

5x + 2y $\leq$ 40

where,

x $\geq$ 0 and y $\geq$ 0

Hence,    

If all the hours are used to produce the product 2 then, the profit will be maximum.

b)

Simply, we can see that the controllable  inputs are product 1 and product 2 or x and y.

and uncontrollable inputs are labor hours here.

c) Flowchart is attached in the attachment below. Please refer to the attachment for the flowchart of the input output process for this model.

d) Optimal solution values for x and y:

If we put the values of the x and y into the equation 10x + 5y, we will get 100 as the objective function. where, x $\geq$ 0 and y $\geq$ 0

Hence, objective function = $100