Linear Programming Problem

The Pyrotec Company produces three small kitchen appliances – waffle makers, egg cookers, and toasters. The three products have the following requirements: Resource Requirements Metal Materials/unit Plastic Materials /unit Labor hours/unit Waffle maker 3.1 lb 0.5 lb .7 Egg cooker 1.5 lb 0.7 lb 1 Toaster 2.0 lb 0.3 lb .5 Resource costs are $3 per pound of metal, $2.90 per pound of plastic and $10.00 per hour for labor. Available resources are 200 pounds of metal, 250 pounds of plastic and 350 hours of labor. Based on market research, the company expects the maximum demand for waffle makers is 50 and for egg cookers is 75. The company has a contract to supply 25 toasters to a local department store. Waffle makers will be sold for 24.99, egg cookers will be sold for 19.99 and Toasters will sell for 14.99 The company wants to know the optimal product mix that will maximize profit. Part A. Write the Linear Programming formulation for this problem to help determine the best production mix of the three appliances that will maximize profit. (25 pts) Part B. Set up & run the problem in Excel Solver. Report the optimal solution and profit result (25 pts)

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(1): Let the decision variables be as follows:   No. made and sold Waffle maker x Egg cooker y Toaster z Now total revenue = 29.99x + 24.99y + 20.99z Total costs of metals = (3.1*x*4)+(1.5*y*4)+(2*z*4) Total cost of plastics = (0.5*x*3.9)+(0.7*y*3.9)+(0.3*z*3.9) Total cost of labor = (0.7*x*11)+(1*y*11)+(0.5*z*11) Objective function = profit = total revenue - total costs = 29.99x + 24.99y + 20.99z - ((3.1*x*4)+(1.5*y*4)+(2*z*4) + (0.5*x*3.9)+(0.7*y*3.9)+(0.3*z*3.9) + (0.7*x*11)+(1*y*11)+(0.5*z*11)) Constraints: 1: 3.1x + 1.5y + 2z <=200 (availability of metal) 2: 0.5x + 0.7y + 0.3z <= 250 (availability of plastic) 3: 0.7x + 1y + 0.5z <= 350 (availability of labor) 4: x <= 50 (max demand for waffle maker) 5: y <= 75 (max demand for egg cooker) 6: z >= 25 (min demand for toaster. Note here that the company has a contract to supply 25 toasters to a store and so it should at least make 25 toasters) Lastly x,y,z should be integers. (2): The solver solution is:   No. made and sold   Waffle maker                                       -     Egg cooker                                72.00   Toaster                                46.00         Total revenue                          2,764.82         Cost of metals                              800.00   Cost of plastic                              250.38   Cost of labor                          1,045.00   Total costs                          2,095.38         Profit                             669.44         Constraints:                       200.00 <=      200.00                     64.20 <=      250.00                     95.00 <=      350.00                            -   <=         50.00                     72.00 <=         75.00                     46.00 >=         25.00 Thus 0 units of waffle maker; 72 units of egg cooker and 46 units of toaster are made and sold. The maximized profit is $669.44 Solver image: q quant 202021 - Microsoft Excel Please upvote ...