Charm City Manufacturing would like to maximize the total profit of producing di
ID: 2944781 • Letter: C
Question
Charm City Manufacturing would like to maximize the total profit of producing dishwasher motors for a major appliance manufacturer. The profit for each model and the time in hours required for each model in each production department is given below.Model 1 Model 2 Model 3
Department A 25 15 22
Department B 10 18 15
Profit 105 85 92
Currently labor availability is 4500 hours in Department A and 2500 hours in Department B. Charm City wants to produce at least 50 of Model 1 motors, at least 50 of Model 2 motors, and at least 50 of Model 3 motors.
Formulate a linear programming model for the above situation by determining
(a) The decision variables (Hint: There are three decision variables for this problem)
(b) The objective function
(c) All the constraints
Note: Do NOT solve the problem after formulating.
Explanation / Answer
Dear Anonymous,
First I will state our decision variables. They are the numbers of the model 1, model 2, and model 3 motors that are made. In particular let us set the variables as below;
a : number of model 1 motors manufactured,
b: number of model 2 motors manufactured,
c: number of model 3 motors manufactured.
Then we may form the objective function, in this case to be maximized, let P stand for profit, then
P = 105a + 85b + 92c
is our objective function to be maximized.
Furthermore, we know that the number of motors that can be manufactured must be at least 50 for each type, thus we have the following three constraints right away:
a 50,
b 50,
c 50.
Furthermore, we know that Department A only has 4500 available labor hours, and that it takes 25 labor hours to produce a model 1 motor, 15 for a model 2 motor, and 22 for a model 3 motor, thus we have the following constraint:
25a + 15b + 22c 4500.
We also know that Department B has only 2500 available labor hours. We also know that it takes 10 hours for Department B to produce a model 1 motor, 18 hours to produce a model 2 motor, and 15 hours to produce a model 3 motor. Thus we have the following relationship:
10a + 18b + 15c 2500.
We have now formulated the entire model. Let me rewrite it for conciseness:
Decision Variables
a : number of model 1 motors manufactured
b: number of model 2 motors manufactured
c: number of model 3 motors manufactured
Objective Function(to be maximized)
P = 105a + 85b + 92c
Constraints
a 50
b 50
c 50
25a + 15b + 22c 4500
10a + 18b + 15c 2500
I hope that this helps!!
David