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Engine Blocks (1000) 500 Plan A B e D E Cost (5 millions) 25 1 33 35 40 20 300 Transmissions (1000) 300 400 800 600 300 400 900 200 The projected needs are for total capacities of 900,000 engine blocks and 900,000 transmissions Management wants to determine which plants to modernize to mett projected manufacturing needs and at the same time, minimize the total cost of modernization. Formulate the integer programming model that could be used to determine the optimal solution to the modemization question facing management Find the optimal solution 4. (10 pts.) The table below indicates the costs (in dollars) of shipping one unit of a certain product from a particular source to a particular destination. The supply at sources 1 and 2 are 10 units and 80 units, respectively. While the demand at destinations 1, 2, and 3 are 30, 20, and 50 units, respectively Source Destination 1 2 Suppose that the penalty costs per unit of unsatisfied demand are S5, S3, and $2 for destinations 1, 2 and 3, respectively. Formulate the linear programming model and determine the optimal solution that would minimize total costs 1/2 2 (0) 3 7 6 6 4 5. (15 pts. The college has planned six special events for its forthcoming alumni homecoming. The table below shows the catering service fees (in thousands of pesos) submitted by seven catering firms based on menu guidelines set by the college for each of the events. 2 V Caterer A B c D E F G 1 126 145 130 115 108 133 125 Event 2 3 103 140 130 165 140 176 126 130 119 129 135 153 100 4 195 170 215 187 175 223 220 $ 250 225 230 262 219 245 267 6 300 320 350 335 285 340 a) Assuming a caterer can service only one event, formulate the integer programming model to determine the optimal selection of caterers that would minimize total cost. Find the optimal solution b) If caterers B, C, and can handle two events, whereas each of the other four caterers can handle only one event, how will you revise your formulation in a? What is the optimal solution? BA 211 Problem Set 1 1. (10 pts.) The Atlantic Seafood Company (ASC) is a buyer and distributor of seafood products that are sold to restaurants and specialty scafood outlets throughout the Northeast ASC has a frozen storage facility in New York City that serves as the primary distribution point for all products. One of the ASC products is frozen large black tiger shrimp, which are sized at 16-20 pieces per pound. Each Saturday, ASC can purchase more tiger shrimp or sell the tiger shrimp at the existing New York City warehouse market price. The ASC goal is to buy tiger shrimp at a low weekly price and sell it later at a higher price, ASC currently has 20,000 pounds of tiger shrimp in storage Space is available to store a maximum of 100,000 pounds of tiger shrimp cach week. In addition, ASC developed the following estimates of tiger shrimp prices for the next four weeks Week Price/b.(5) 1 2 6.00 6.20 3 4 6,655 55 ASC would like to determine the optimal buying storing-selling strategy for the next four weeks The cost to store a pound of shrimp for one week is $0.15, and to account for unforeseen changes in supply or demand, management also indicated that 25.000 pounds of tiger shrimp must be in storage at the end of week 4. Formulate the linear programming model and determine the optimal buying-storing-selling strategy for ASC 2. (15 p.) Metro Food Services Company delivers fresh sandwiches each morning to vending machines throughout the city. The company makes three kinds of sandwiches - ham and cheese, bologna, and chicken salad. A ham and cheese sandwich requires a worker 0.45 minutes to assemble, a bologna sandwich requires 0.41 minutes, and a chicken salad sandwich requires 0.50 minutes to make. The company has 16 hours available cach night for sandwich assembly. Vending machine capacity is available for 2,000 sandwiches cach day. The profit for a ham and cheese sandwich is $0.35, the profit for a bologna sandwich is $0.42, and the profit for a chicken salad sandwich is $0.37. The company knows from past sales records that its customers buy as many as ham and cheese sandwiches as the other two sandwiches combined, if not more so, but customers need a variety of sandwiches available, so Metro stocks at least 200 of each. Metro management wants to know how many of each sandwich it should stock to maximize profit. a) Formulate the linear programming model for this problem. b) Find the optimal solution. c) If Metro Food Services could hire other worker and increase its available assembly time by 8 hours or increase its vending machine capacity by 100 sandwiches, which should it do? Why? How much additional profit would your decision result in? d) What would be the effect on the optimal solution if the profit for a ham and cheese sandwich was increased to $0.407 c) Would it be more profitable to stock at least 300 chicken salad sandwiches instead of 2007 Justify 3. (10 p.) An automobile manufacturer has five outdated planta A, B, C, D, and E. Management considering modemizing these plants to come black and transmissions for a new model car. The cost to modernize each plant and the facturing capacity after moderation are follow