Pizza - Another DMOR Sensitivity Analysis Example My Family...

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Another DMOR Sensitivity Analysis Example 10/02/07 My Family owns an Italian restaurant, even though they only know how to make three Italian dishes: pizza, cheese sticks, and calzones. They would like to determine how much of each food product to make. Each food consists of dough, sauce, and cheese. We have 20 units of dough, 10 units of sauce, and 40 units of cheese available to us. Consider the following grid of resource utilization by each food, and price for which they can sell the food. FOOD Dough consumption Sauce consumption Cheese consumption Price Pizza 1 1 3 $10 Cheese sticks 2 0 1 $6 Calzones 2 1 1 $8 We can thus model this problem as the following linear program, where x 1 is the amount of pizza produced, x 2 is the amount of cheese sticks produced, and x 3 is the amount of calzones produced: Maximize 10 x 1 + 6 x 2 + 8 x 3 Subject to x 1 + 2 x 2 + 2 x 3 20 (dough) x 1 + x 3 10 (sauce) 3 x 1 + x 2 + x 3 40 (cheese) x 0 After optimizing this problem, we have the following optimal simplex tableau. Basics z x 1 x 2 x 3 s 1 s 2 s 3 RHS 1 0 0 5 3 7 0 130 x 2 0 0 1 1/2 1/2 -1/2 0 5 x 1 0 1 0 1 0 1 0 10 s 3 0 0 0 -5/2 -1/2 -5/2 1 5 Question a. What are the shadow prices of each constraint? Question b. Right now, x 3 = 0 and so we don’t want to produce any calzones. Paulie believes that if we increase the price of calzones, it will become optimal to sell them.
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