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Question: use linear programming to determine how ppco can maximize profits...

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Paris Perfume Company (PPCo) produces a fragrance for women (W) and another for men (M); both of them require chemicals and labor. Two production processes are available: Process 1 produces 50-ml. bottles; Process 2 produces 125-ml. bottles. To make one hundred bottles of W in Process 1 requires 1,500 ml of Chemical 1;2,250 ml of Chemical 2; and 1.7 hours of labor. To make one hundred bottles of W in Process 2 requires 3,750 ml of Chemical 1; 5,625 ml of Chemical 2; and 2.5 hours of labor. To make one hundred bottles of M in Process 1 requires 2 liters of Chemical 1; 1 liter of Chemical 2, and 1.5 hours of labor. To make one hundred bottles of M in Process 2 requires 5 liters of Chemical 1; 2.5 liters of Chemical 2, and 2 hours of labor. It costs PPCo $30 to purchase one hour of labor; $1000 to purchase a litter of Chemical 1 and $1500 to purchase a litter of Chemical 2. Each year, up to 1,200 hours of labor and 2000 liters of Chemical 1 and 1500 liters of Chemical 2 can be purchased. PPCo believes it can sell up to 6000 liters of perfume annually; but the amount of perfume for men never exceeds the total amount for women. Each ml of W sells for $1.25 and each ml of M sells for $1.00. (a) Define the decision variables; be sure to identify the units of the decision variables. (b) Write out the linear programming formulation of the problem. Include the units of the variables and the coefficients in your description. (c) Solve the problem from part (b) using Excel; attach a printout of your Excel spreadsheet and clearly explain your optimal solution in terms of the wording of this situation. 1. 9

Use linear programming to determine how PPCo can maximize profits.

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