Exercisel(а):What do you mean by Linear Programming Problem? Write the general form of an LPP.(b):Cycle Trends is introducing two new lightweight bicycle frames, the Deluxe and the Professional,to be made from aluminum and steel alloys. The anticipated unit profits are SAR 30 for the Deluxeand SAR 35 for the Professional.The number of pounds of each alloy needed per frame is summarized in the following table. Asupplier delivers 90 pounds of the aluminum alloy and 100 pounds of the steel alloy weekly. Howmany Deluxe and Professional frames should Cycle Trends produce each week?Table: Pounds of each alloy needed per frameFrameAluminum AlloySteel AlloyDeluxe43Professional34Formulate the above problem as linear programming problem.

(a) We have to define the Linear programming problem,

Answered: Exercisel (а): What do you mean by…

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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An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $     . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $     per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…
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.
What is the correct way to write out the non-linear program for part a?
(a) The WorldLight company produces two light fixtures (product A and Product B) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product A, 1 unit of frame parts and 2 unit of electrical components are required. For each unit of product B, 3 unit of frame parts and 2 unit of electrical components are required. The company has 200 units of frame parts and 300 units of electrical components. Each unit of product A gives a profit of 1 dollars, and each unit of product B up to 60 units, gives a profit of 2 dollars. any excess over 60 units of product B brings no profit, so such an excess has been ruled out. Formulate a linear programming model for this problem. (b) Consider the following linear programming problem. Minimize Z = 8rı + 5a2 subject to -3.r1 + 2r2 < 30 2x1 + 12 2 50 Iị + 12 2 30 and 21 20, x2 2 0. Solve this problem graphically.
Formulate 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 5500 televisions/month, whereas the output at Location II is at most 4700 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 2600 and 3700 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. From TMA Location I Location II Minimize 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 companies while keeping costs, C (in dollars), to a minimum.…
Use Excel to solve the linear programming problem.At one of its factories, a manufacturer of televisions makes one or more of four models of HD units (without cases): a 20-in. LCD, a 42-in. LCD, a 42-in. plasma, and a 50-in. plasma. The assembly and testing time requirements for each model are shown in the table, together with the maximum amounts of time available per week for assembly and testing. In addition to these constraints, the supplier of cases indicated that it would supply no more than 290 cases per week and that of these, no more than 40 could be for the 20-in. LCD model.Use the profit for each television shown in the table to find the number of completed models of each type that should be produced to obtain the maximum profit for the week. Find the maximum profit. 20-in. LCD sets 42-in. LCD sets 42-in. plasma sets 50-in. plasma sets profit $ 20-in.LCD 42-in.LCD 42-in.Plasma 50-in.Plasma TotalAvailable Assembly time…
Formulate 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--

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