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Presentation/PPT
27/08/2022
4 A diet is being prepared for the University of Arizona dorms. The objective is to feed the students at the least cost, but the diet must have between 1,800 and 3,600 calories. No more than 1,400 calories can be starch, and no fewer than 400 can be protein. The varied diet is to be made of two foods: A and B. Food A costs $0.75 per pound and contains 600 calories, 400 of which are protein and 200 starch. No more than two pounds of food A can be used per resident. Food B costs $0.15 per pound and contains 900 calories, of which 700 are starch, 100 are protein, and 100 are fat.a. Write the equations representing this information.b. Solve the problem graphically for the amounts of each food that should be used.5 Do Problem 4 with the added constraint that not more than 150 calories shall be fat andthat the price of food has escalated to $1.75 per pound for food A and $2.50 per pound for food B.6 Logan Manufacturing wants to mix two fuels, A and B , for its trucks to minimize cost. It needs no fewer than 3,000 gallons to run its trucks during the next month. It has a maximum fuel storage capacity of 4,000 gallons. There are 2,000 gallons of fuel A and 4,000 gallons of fuel B available. The mixed fuel must have an octane rating of no less than 80. When fuels are mixed, the amount of fuel obtained is just equal to the sum of the amounts put in. The octane rating is the weighted average of the individual octanes, weighted in proportion to the respective volumes.The following is known: Fuel A has an octane of 90 and costs $1.20 per gallon. Fuel B has an octane of 75 and costs $0.90 per gallon.a. Write the equations expressing this information.b. Solve the problem using the Excel Solver, giving the amount of each fuel to be used. State any assumptions necessary to solve the problem.7 You are trying to create a budget to optimize the use of a portion of your disposable income. You have a maximum of $1,500 per month to be allocated to food, shelter, and entertainment. The amount spent on food and shelter combined must not exceed $1,000. The amount spent on shelter alone must not exceed $700. Entertainment cannot exceed $300 per month. Each dollar spent on food has a satisfaction value of 2, each dollar spent on shelter has a satisfaction value of 3, and each dollar spent on entertainment has a satisfaction value of 5. Assuming a linear relationship, use the Excel Solver to determine the optimal allocation of your funds.9 BC Petrol manufactures three chemicals at their chemical plant in Kentucky: BCP1, BCP2, and BCP3. These chemicals are produced in two production processes known as zone and man. Running the zone process for an hour costs $48 and yields three units of BCP1, one unit of BCP2, and one unit of BCP3. Running the man process for one hour costs $24 and yields one unit of BCP1 and one unit of BCP2. To meet customer demands, at least 20 units of BCP1, 10 units of BCP2, and 6 units of BCP3 must be produced daily. Assuming a linear relationship, use Excel Solver to determine the optimal mix of processes zone and man to minimize costs and meet BC Petrol daily demands
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