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 40
where,
x 0 and y 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 0 and y 0
Hence, objective function = $100