Incline Electronics produces three different products in a plant that is open 40 hours per week. Each product requires the following processing times (in hours) on each of three machines. Product 1 Product 2 Product 3
Machine 1 2 2 1
Machine 2 3 4 6
Machine 3 4 6 5
Each machine must be run by one of 19 cross-trained workers who are each available 35 hours per week. The plant has 10 type 1 machines available, 6 type 2 machines available, and 8 type 3 machines available. Products 1, 2, and 3 contribute $90, $120, and $150, respectively, in marginal profit per unit produced.
a. Select the correct LP model for this problem.
Let P1 represent Units of product 1 to make.
Let P2 represent Units of product 2 to make.
Let P3 represent Units of product 3 to make.
I. IMAX 90P1 + 120P2 150P3
ST 2P1 + 2P2 + 1P3 < or equal to 240
3P1 + 4P2 + 6P3 < or equal to 400
4P1 + 6P2 + 5P3 < or equal to 320
Pi > or equal to 0
II. MIN 9P1 + 120P2 + 150P3
ST 2P1 + 2P2 + 1P3 < or equal to 240
3P1 + 4P2 + 6P3 < or equal to 320
4P1 + 6P2 + 5P3 < or equal to 400
9P1 + 12P2 + 12P3 < or equal to 665
Pi > 0
III. MIN 90P1 + 120P2 + 1S0P3
ST 2P1 + 2P2 + 1P3 < or equal to 2 400
3P1 + 4P2 + 6P3 < or equal to 669
4P1 + 6P2 + 5P3 < or equal to 320
9P1 + 12P2 + 12P3 < or equal to 240
Pi > 0
P1 12P2+12P3 S 665
IV. MAX 90Pi + 120P2 + 150P3
ST 2P + 2P2 + 1P3 < or equal to 400
3P1 + 4P2 + 6P3 < or equal to 240
4P1 + 6P2 + 5P3 < or equal to 320
Pi > or equal to 0
b. Implement your model in a spreadsheet and solve it. How many units for each product should Incline Electronics produce?
c. What is the optimal solution?