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BUSI 410 – MIDTERM ANSWERS WITH GRADING COMMENTS Designing Meals at Panera Bread a. (8 points) What are the decision variables? (state in English & define symbols to represent them) C = the number of grams of grilled chicken in the meal S = the number of grams of salad in the meal U = the number of grams of soup in the meal B = the number of grams of bread in the meal b. (3 points) What are the objective function and the objective criterion (maximize or minimize)? (State in English and provide the mathematical equation) The goal is the minimize the preparation cost of the meal: min 0.05C + 0.02S + 0.04U + 0.01B c. (7 points) What are the constraints? (State in English and provide the mathematical equations) The meal has no more than 600 kcal: 15C + 5S + 10U + 8B ≤ 600 The meal has at least twice as much fiber as protein: 20S + 5U + 10B ≥ 2 (15C + 10U + 3B) or -30C + 20S – 15U + 4B ≥ 0 Grilled chicken is at least 30% of the total weight: C ≥ 0.3 (C + S + U + B) or 0.7C – 0.3S – 0.3U – 0.3B ≥ 0 Grilled chicken is at most 20% of the total preparation cost: 0.05C ≤ 0.2 (0.05C + 0.02S + 0.04U + 0.01B) or 0.04C -0.004S – 0.008U – 0.002B ≤ 0 Non-negativity: C ≥ 0, S ≥ 0, U ≥ 0, and B ≥ 0

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Part B. (3 points) Suppose you solve the problem you formulated in part A and find that the optimal meal has exactly twice as much fiber as protein. Recently Panera has experienced a shortage in vegetables, which are Panera Bread’s main source of fiber. In response, Panera Bread decides to temporarily remove the requirement that the meal has at least twice as much fiber as protein, and it asks you to redesign the meal. How will the (optimal) preparation cost of the new meal compare to that of the original meal in part A? Explain. Each constraint added to the formulation further restricts the possible values of the decision variables, and thus “penalizes” the value of the objective function. Thus, adding a constraint would increase the minimum cost if the constraint further restricts
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