It is the nature of the restrictions imposed on the decisions regarding the mix of activity levels that determines the classification of the resulting linear programming formulation. O True O False
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- Formulate but do not solve the following exercise as a linear programming problem. Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $12,000/day to operate, and it yields 45 oz of gold and 3000 oz of silver each of x days. The Horseshoe Mine costs $14,000/day to operate, and it yields 80 oz of gold and 1250 oz of silver each of y days. Company management has set a target of at least 600 oz of gold and 16,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost C in dollars? Minimize C = subject to the constraints gold silverFormulate but do not solve the following exercise as a linear programming problem.National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A cost $120 to make, and each model B costs $150. The profits are $30 for each model A and $30 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 1900 and the company has earmarked not more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profits P in dollars ? Maximize P = subject to the constraints manufacturing costs number produced x ≥ 0 y ≥ 0A) The ABC engineering organization is supposed to carry out 5 types of repairs through five different operations. The table below gives the time required per each repair, the daily repair capacity of the operations and the profit gained per each repair.Formulate the problem as a linear programming model to maximize the profit. Operation Time per repair(minute) time Operations min/day F G H I J A 20 10 12 30 18 400 В 30 28 11 13 410 C 15 19 24 26 420 D 27 13 37 14 430 E 30 29 27 17 20 415 Profit 20 19 21 18 17 /repair
- Formulate but do not solve the following exercise as a linear programming problem.A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3 on each unit of Product A and $5 on each unit of Product B. To manufacture a unit of Product A requires 5 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 5 min on Machine II. There are 269 min available on Machine I and 205 min available on Machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P in dollars? Maximize P = subject to the constraints Machine I Machine II x ≥ 0 y ≥ 01. Set up a linear programming model of the situation described. Determine whether it is in standard 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 protein The 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 many kilograms of each food should be served so as to maximize his profit?Choose Yes or No to indicate whether each of the following statements about the CONVEXITY OR CONCAVITY of an OBJECTIVE FUNCTION of convex programming problems is true. Objective function may exist and may be concave Objective function may exist and may be convex Objective function may exist and may be neither convex nor concave Objective function may exist and must be concave Objective function may exist and must be convex Objective function may exist and must be neither convex nor concave Objective function must exist and must be concave Objective function must exist and must be convex Objective function must exist and must be neither convex nor…
- Formulate but do not solve the following exercise as a linear programming problem. A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. She has decided that the meals are to be prepared from Foods A and B and that the meals should contain a minimum of 390 mg of calcium, 10 mg of iron, and 40 mg of vitamin C. Each ounce of Food A contains 25 mg of calcium, 2.5 mg of iron, 2 mg of vitamin C, and 6 mg of cholesterol. Each ounce of Food B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol. How many ounces of each type of food should be used in a meal so that the cholesterol content C (in mg) is minimized and the minimum requirements of calcium, iron, and vitamin C are met? Minimize C = subject to the constraints calcium iron vitamin C x ≥ 0 y ≥ 0Formulate but do not solve the following exercise as a linear programming problem.TMA manufactures 37-in. high-definition LCD televisions in two separate locations: Location I and Location II. The output at Location I is at most 6500 televisions/month, whereas the output at Location II is at most 5300 televisions/month. TMA is the main supplier of televisions to Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 3600 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the two TMA plants to the two Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $6 $4 Location II $8 $7 TMA will ship x televisions from Location I to City A and y televisions from Location I to City B. Find a shipping schedule that meets the requirements of both…Formulate a linear programming problem that can be used to solve the following question. A firm has plants in Boston and Baltimore that manufacture three models of hot tubs: regular, fancy, and super. In one day the Boston plant can manufacture 44 of the regular model, 32 of the fancy model, and 20 of the super model, and costs $4500 per day to operate, whereas the Baltimore plant can manufacture 12 of the regular model, 16 of the fancy model, and 58 of the super model, and costs $2000 per day to operate. At least 300 of the regular model, 320 of the fancy model, and 680 of the super model are needed. How many days must each plant operate in order to minimize the cost? ---1pəjəs-- = X y = ---Select--- ---Select--- v F = (objective function) Subject to (regular models) (fancy models) (super models) 0A---1pajas--
- Is there any "real world" implementation of dynamic programming?The contribution to profits and overhead per 100 feet of pipe is $34 for type 1 and $40 for type 2.- Formulate a linear programming model to determine how much of each type of pipe should be produced to maximize contribution to profits and to overhead, assuming that everything produced can be sold.- Find the optimal solution algebraically for the Moldex Company problem. What is the Z value when the decision variables have optimal values?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.