Mat 540 Extra Credit Assignment Please show all work, whereappropriate! 1. Gillianâs Restaurant has an ice-cream counter whereit sells two main products, ice cream and frozen yogurt, each in avariety of flavors. The restaurant makes one order for ice creamand yogurt each week, and the store has enough freezer space for115 gallons total of both products. A gallon of frozen yogurtcost$0.75 and a gallon of ice cream costs $0.93, and the restaurantbudgets $90 each week for these products. The manager estimatesthat each week the restaurant sells at least twice as much icecream as frozen yogurt. Profit per gallon of ice cream is $4.15,and profit per gallon of yogurt is $3.60. a. Formulate a linearprogramming model for this problem. b. Solve this problem by usingthe computer. 2. United Aluminum Company of Cincinnati producesthree grades (high, medium, low) of aluminum at two mills. Eachmill has a different production capacity (in tons per day) for eachgrade, as follows: Mill Aluminum Grade 1 2 High 6 2 Medium 2 2 Low4 10 The company has contracted with a manufacturing firm to supplyat least 12 tons of high-grade aluminum, 8 tons of medium-gradealuminum, and 5 tons of low-grade aluminum. It costs United $6,000per day to operate mill 1 and $7,000 per day to operate mill 2. Thecompany wants to know the number of days to operate each mill tomeet the contract at minimum cost. a. Formulate a linearprogramming model for this problem. b. Solve this problem by usingthe computer. 3. Betty Malloy, owner of the Eagle Tavern inPittsburgh, is preparing for Super Bowl Sunday, and she mustdetermine how much beer to stock. Betty stocks three brands of beerâ Yodel, Shotz, and Rainwater. The cost per gallon (to the tavernowner) of each brand is as follows: Brand Cost/gallon Yodel $1.50Shotz 0.90 Rainwater 0.50 The tavern has a budget of $2,000 forbeer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 pergallon. Based on past football games, Betty has determined themaximum customer demand to be 400 gallons of Yodel, 500 gallons ofShotz, and 300 gallons of Rainwater. The tavern has a capacity tostock 1,000 gallons of beer; Betty wants to stock up completely.Betty wants to determine the number of gallons of each brand ofbeer to order so as to maximize profit. a. Formulate a linearprogramming model for this problem. b. Solve this problem by usingthe computer. 4. A jeweler and her apprentice make silver pins andnecklaces by hand. Each week they have 80 hours of labor and 36ounces of silver available. It requires 8 hours of labor and 2ounces of silver to make a pin, and 10 hours of labor and 6 ouncesof silver to make a necklace. Each pin also contains a small gem ofsome kind. The demand for pins is no more than six per week. A pinearns the jeweler $400 in profit, and a necklace earns $100. Thejeweler wants to know how many of each item to make each week tomaximize profit. a. Formulate an integer programming model for thisproblem. b. Solve this problem by using the computer. 5. Atransportation problem involves the following costs, supply anddemand. To From 1 2 3 4 Supply 1 $500 $750 $300 $450 12 2 650 800400 600 17 3 400 700 500 550 11 Demand 10 10 10 10 a. Formulate alinear programming model for this problem. b. Solve thistransportation problem by using the computer.
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