1. Leather Limited manufactures two types of belts: the deluxe model and the regular model.Each type requires 1 square meter of leather. A regular belt requires 1 hour of skilled labor,and a deluxe belt requires 2 hours. Each week, 40 square meter of leather and 60 hours ofskilled labor are available. Each regular belt contributes USD 3 to profit and each deluxe belt,USD 4.(a) State the problem in a formal Linear Programming equations!(b) Solve the problem using Simplex method!(c) Write down your conclusion from the optimal solution that you have.(d) To improve the total profit of the company, is it better to increase the inventory ofleather per week, or to increase the availability of skilled labor per week? Explain!

(a) Suppose, the number of deluxe belts and regular belts be x,y respectively. Suppose, the total…

Answered: 1. Leather Limited manufactures two…

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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Formulate 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 ≥ 0
Solve the following linear programming problem. You are taking two dietary supplements daily: Supplement A and Supplement B. An ounce of supplement A contains 9 units of calcium, 8 units of vitamin D, and 5 units of sodium. An ounce of supplement B contains 2 units of calcium, 4 units of vitamin D, and 3 units of sodium. Your goal is to get at least 90 units of calcium and at least 120 units of vitamin D from the supplements daily, while at the same time reducing the amount of sodium that you will get. How many ounces of each supplement should you take daily to reach your goals? Ounces of Supplement A = Blank 1. Fill in the blank, read surrounding text. Ounces of Supplement B = Blank 2. Fill in the blank, read surrounding text. How many units of sodium will you get daily under these circumstances? Units of Sodium = Blank 3. Fill in the blank, read surrounding text.
company manufactures bamboo toy chairs and chess sets. Each bamboo toy chair yields a profit of $3, and each chess set, $5. A bamboo toy chair requires 5 hours of processing at Machine A and three hours at Machine B, and one hour at Machine C, while a chess set requires seven hours at Machine A, sixhours at Machine B, and two hours at Machine C.Machine A has a maximum of 130 hours of available capacity per day. Machine B has 90 hours, and Machine C has 25 hours.If the company wishes to maximize profit, how many bamboo toy chairs and chess sets should be produced per day?
Formulate a linear programming problem that can be used to solve the following question. An airline has three types of airplanes and has contracted with a tour group to provide transportation for a minimum of 70 first-class, 52 tourist, and 108 economy-class passengers. The first plane costs $4100 for the trip and can accommodate 36 first-class, 16 tourist, and 18 economy-class passengers; the second plane costs $4800 for the trip and can accommodate 8 first-class, 10 tourist, and 42 economy-class passengers; the third plane costs $6300 for the trip and can accommodate 18 first-class, 36 tourist, and 16 economy-class passengers. How many of each type of airplane should be used to minimize the operating cost? X = ---Select--- y = ---Select--- ---Select--- Z |||| ---Select--- | F = AC UB Subject to X ---Select--- 0, y ---Select--- (objective function) (first-class passengers) (tourist passengers) (economy-class passengers) 0, z ---Select--- 0 (nonnegativity constraint)
Bata Aerobics manufactures two models of steppers used for aerobic exercises, x number of luxury models and y number of standard models. Manufacturing each luxury model requires 10 lb of plastic and 10 min of labor. Manufacturing each standard model requires 16 lb of plastic and 8 min of labor. The profit for each luxury model is $50, and the profit for each standard model is $35. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day in order to maximize its profit? (x, y) = What is the optimal profit?$
Write the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)
Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 380 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 34 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 29 ounces. Unfortunately, food I contains 22 units of cholesterol per ounce and food II contains 32 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = ---Select--- y = --Select--- ---Select--- | F = Subject to (objective function) (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)
which options are correct ?
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--
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)

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