代写Assignment 3代做留学生SQL语言

日期：2024-03-29 02:12

Please submit BOTH your answers and excel file.

Problem 1 (Mayor)

(Isoprofit method) A candidate for mayor in a small town has allocated $45,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $300 and reaches an estimated 3,000 people. Each television ad costs $600 and reaches an estimated 5,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach? Formulate the linear programming problem and solve it by isoprofit method.

Problem 2 (Woofer Pet Foods)

(Corner solutions) Woofer Pet Foods produces a low-calorie dog food for overweight dogs. This product is made from beef products and grain. Each pound of beef costs $0.90, and each pound of grain costs $0.60. A pound of the dog food must contain at least 9 units of Vitamin 1 and 10 units of Vitamin 2. A pound of beef contains 10 units of Vitamin 1 and 12 units of Vitamin 2.A pound of grain contains 6 units of Vitamin 1 and 9 units of Vitamin 2. Formulate this as an LP problem to minimize the cost of the dog food and solve it using corner points method. How many pounds of beef and grain should be included in each pound of dog food? What is the cost and vitamin content of the final product?

Problem 3

(Graphical Method) Graphically solve the following problem:

Maximize profit = 8 X1  + 5 X2

X1 + X2 ≤ 10 (1)

X1 ≤ 6 (2)

X1, X2 ≥ 0

a) What is the optimal solution?

b) Change the right-hand side of constraint (1) from 10 to 11 and resolve the problem. How much did the profit change as a result of this?

c) Change the right-hand side of constraint (1) to 6 (instead of 10) and resolve the problem. How much   did the profit change as a result of this? Looking at the graph, what would happen to constraint (2) if the right-hand-side value of the constraint (1) were to go below 6?

Problem 4 (Kathy Roniger’s Mean Plan)

(Use Excel Solver) Kathy Roniger, campus dietitian for a small Idaho college, is responsible for formulating a nutritious meal plan for students. For an evening meal, she feels that the following five meal-content requirements should be met: (1) between 900 and 1,500 calories; (2) at least 4 miligrams of iron; (3) no more than 50 grams of fat; (4) at least 26 grams of protein; and (5) no more than 50 grams of carbohydrates. On a particular day, Roniger’s food stock includes seven items that can be prepared and served for supper to meet  these requirements. The cost per pound for each food item and the contribution to each of the five nutritional requirements are given in the table below.

What combination and amounts of food items will provide the nutrition Roniger requires at the least total food cost?

(a) Formulate this as an LP problem, put it in Excel and use the Solver to solve it.

(b) What is the cost per meal?

(c) Generate the sensitivity report in excel and explain how would an increase in milk price by 10 cents/lb impact your decision.

(d) How much can you change the milk price before the optimal solution changes?

Problem 5 (Triangle Utilities)

(Using Excel Solver) Triangle Utilities provides electricity for three cities. The company has four electric generators that are used to provide electricity. The main generator operates 24 hours per day, with an occasional shut-down for routine maintenance. Three other generators (1, 2, and 3) are available to provide additional power when needed. A start-up cost is incurred each time one of these generators is started. The start-up costs are $6,000 for 1, $5,000 for 2, and $4,000 for 3. These generators are used in one of the following ways: a generator may be started at 6:00 a.m. and run for either 8 hours or 16 hours, or it may be started at 2:00 p.m. and run for 8 hours (until 10:00 p.m.). Each generator can only be started once. All generators except the main generator are shut down at 10:00 p.m. Forecasts indicate the need for 3,200 megawatts more than provided by the main generator before 2:00 p.m., and this need goes up to 5,700 megawatts between 2:00 and 10:00 p.m. During each 8-hour period, generator 1 may provide up to 2,400 megawatts, generator 2 may provide up to 2,100 megawatts, and generator 3 may provide up to 3,300 megawatts. The cost per megawatt used per 8-hour period is $8 for 1, $9 for 2, and $7 for 3.

(a)  Formulate this problem as a mixed integer program to determine the least-cost way to meet the needs of the area.

(b)  Solve the problem formulated in (a) by Excel solver.