Charming City manufacturing would like to maximize the total profit of producing
ID: 393429 • Letter: C
Question
Charming City manufacturing would like to maximize the total profit of producing two products: Product A and Product B. The profit in dollars, the material units, the labor hours and the processing hours required for one unit of each product are given below.
Product A
Product B
Material
30
18
Labor
12
20
Processing
10
10
Profit
80
65
Currently the material availability is 5000 units, the labor availability is 4000 hours and the processing availability is 2500 hours. Charming City wants to produce at least 100 of Product A and at least 85 of Product B.
Formulate a linear programming model for the above situation by determining
(a) The decision variables
(b) Determine the objective function. What does it represent?
(c) Determine all the constraints. Briefly describe what each constraint represents.
Note: Do NOT solve the problem after formulating.
Product A
Product B
Material
30
18
Labor
12
20
Processing
10
10
Profit
80
65
Explanation / Answer
a) Decision variables are:
Quantity of Product A = 'A'
Quantity of Product B = 'B'
b) Objective function:
Maximize Profit Z = 80*A + 65*B
c) Constraints:
Material: 30A + 18B <= 5000
Labor: 12A + 20B <= 4000
Processing: 10A + 10B <= 2500
The constraints represents the limiting factor for linear programming model. Example: The maximum labor hours possible are 4000 which is a sum product value of Product A & B.