Problem . Solve the following problem.
A company produces two products, A, B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows:
|
Hours/Unit
|
|
Product
|
Line 1
|
Line 2
|
|
A
|
12
|
4
|
|
B
|
4
|
8
|
|
Total Hours
|
60
|
40
|
1. Formulate an LP programming model of the above problem to determine the optimal product mix that will maximize profit.
1.1. Transform the model into standard form.
1.2. Solve the Problem Graphically
1.2.1. Identify the amount of unused resources (i.e. slack) at each of the extreme points.
1.2.2. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours?
1.2.3. What would be the effect on the optimal solution of the profit for product B was increased from a) $7 to $15? B) to $20?
1.3. Solve the LP problem using the Excel Solver
1.3.1. What is the Optimal Profit?
1.3.2. What are the values of the variables and slacks at the optimal solution?
1.3.3. What is the range of each objective function coefficient?
1.3.4. What is the range of each resource?
1.3.5. Which are the binding constraints?