1. Set up a linear programming model of the situation described. Determine whether it is instandard form. If not make it standard.A restaurant chef is planning a meal consisting of two foods, A, and B.• Each kg of A contains 3 units of fat and 6 units of protein• Each kg of B contains 1 unit of fat and 3 units of proteinThe chef wants the meal to consist of at least 18 units of protein and at most 6 units of fat.If the profit that he makes is 3 dollars per kg for food A and 5 dollars for food B, how manykilograms of each food should be served so as to maximize his profit?

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Answered: 1. Set up a linear programming model of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Q2: A/ The Middle East Company manufactures two types of packing tins- red & black. Major production facilities involved are cutting and joining. The cutting department can process 200 red tins or 400 black tins per hour. The joining department can process 400 red tins or 200 black tins per hour. If the contribution towards profit for a red tin is the same as that of a black tin, what is the optimal production level? Formulate a linear programming model for this problem.
Which of the following is not true about linear programming? The value of the variables can be negative. The objective is either to maximize or to minimize. The relationship between variables can be expressed in equations or inequalities. The actions are constrained.
Set-up and solve the following linear programming problem. A dietician is preparing a special diet using two foods: Food X and Food Y. Each unit of Food X provides 1 gram of protein, 1 gram of fat, and 4 grams of carbohydrates, and it contains 25 calories. Each unit of Food Y provides 5 grams of protein, 1 gram of fat, and 2 grams of carbohydrates, and it contains 50 calories. Her goal is to use the two foods to prepare a meal providing at least 40 grams of protein, at least 16 grams of fat, and at least 48 grams of carbohydrates. Determine the number of units of each food she should use to meet her nutritional requirements and minimize the number of calories. What is the minimum number of calories? The number of units of Food X is Blank 1. Fill in the blank, read surrounding text. units. The number of units of Food Y is Blank 2. Fill in the blank, read surrounding text. units. The minimum number of calories is Blank 3. Fill in the blank, read surrounding text.…
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The supplies, demands, and transportation costs per unit are shown on the network. (a)Develop a linear programming model for this problem; be sure to define the variables in your model. Let x11 = amount shipped from Jefferson City to Des Moines x12 = amount shipped from Jefferson City to Kansas City x13 = amount shipped from Jefferson City to St. Louis x21 = amount shipped from Omaha to Des Moines x22 = amount shipped from Omaha to Kansas City x23 = amount shipped from Omaha to St. Louis Min ???????? s.t. From Jefferson City ?????? From Omaha ??????? To Des Moines ??????? To Kansas City ???????? To St. Louis ???????????? x11, x12, x13, x21, x22, x23 ≥ 0 (b)Solve the linear program to determine the optimal solution. Amount Cost Jefferson City–Des Moines Jefferson City–Kansas City Jefferson City–St. Louis Omaha–Des Moines Omaha–Kansas City Omaha–St. Louis Total
Formulate a linear programming problem that can be used to solve the following question. A dealer has 8900 pounds of peanuts, 6000 pounds of almonds, and 3800 pounds of cashews to be used to make two mixtures. The first mixture wholesales for $2.40 per pound and consists of 60% peanuts, 30% almonds, and 10% cashews. The second mixture wholesales for $3.20 per pound and consists of 15% peanuts, 45% almonds, and 40% cashews. How many pounds of each mixture should the dealer make to maximize revenue? x = ---Select--- y = ---Select--- ---Select--- v|F= Subject to (objective function) (pounds of peanuts) (pounds of almonds) (pounds of cashews) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
A farmer wishes to buy some goats and cows. He has pasture for only 50 animals. Goats cost $300 each and cows $600 each. He can expect to make a profit of $250 on each goat and $350 on each cow. If he has $24000 to spend and he buys g goats and c cows, I. Formulate a linear programming model for this situation. II. Using a graph, find the numbers of goats and cows that will maximize profit. III. State the maximum profit.
Explain important characteristics of situations to which linear programming method can be successfully applied. Assume a suitable example A firm manufactures three products A, B, and Time to manufacture product A is twice that for B and thrice that for C and if the entire labour is engaged in making product A, 1,600 units of this product can be produced. These products are to be produced in the ratio 3:4:5. There is demand for at least 300, 250 and 200 units of products A, B and C and the profit earned per unit is sh. 90, sh. 40 and sh. 30 respectively. Table Raw material Requirement per unit of product (kg) Total availability (kg) A B C P 6 5 2 5,000 Q 4 7 3 6,000 Formulate the problem as a linear programming problem.

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