Exercise 2.9A company manufactures two products X and Y. The profit contribution of X and Y are$.3/- and $4/- respectively. The products X and Y require the services of four facilities. Thecapacities of the four facilities A, B, C, and D are limited and the available capacities in hours are 200Hrs, 150 Hrs, and 100 Hrs. and 80 hours respectively. Product X requires 5, 3, 5 and 8 hours offacilities A, B, C and D respectively. Similarly the requirement of product Y is 4, 5, 5, and 4 hoursrespectively on A, B, C and D. Find the optimal product mix to maximise the profit.

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Answered: Exercise 2.9 A company 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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A company produces two types of hand soaps: a solid and a liquid soap. The cost of production for a solid soap is 10 cents per soap and 20 cents for the liquid soap. The company developed a model that predicts how many units x1 (of the solid soap), and x2 (of the liquid soap) they will sell per month. According to the model, the amount of units sold depends on the prices p1,p2 (in dollars) of solid and liquid soap through the equations ( see attached for equation) Set up a function to describe how the total profit (revenue - costs) depends on the unit prices p1 and p2.
A grocery store sells two brands of a product, the "house" brand and a "name" brand. The manager estimates that if she sells the "house" brand for x dollars and the "name" brand for y dollars, she will be able to sell 63 – 10x + 21y units of the "house" brand and 40 + 13x – 10y units of the "name" brand. Step 1 of 2: Find the revenue function R(x, y).
A brewery produces regular beer and a lower-carbohydrate "'light" beer. Steady customers of the brewery buy 12 units of regular beer and 18 units of light beer monthly. While setting up the brewery to produce the beers, the management decides to produce extra beer, beyond that needed to satisfy customers. The cost per unit of regular beer is $32,000 and the cost per unit of light beer is $60,000. Every unit of regular beer brings in $100,000 in revenue, while every unit of light beer brings in $300,000 in revenue. The brewery needs at least $9,000,000 in revenue, and has determined that the total demand will be at least 50 units of beer. Complete parts (a) and (b). (a) How much of each type of beer should be made so as to minimize total production costs? ◻️units of regular beer and◻️ units of light beer should be made, for a minimum total cost of $◻️
A company produces 3 products. Each unit of product 1, 2, and 3 generate a profit of GH₵10, GH₵12, and GH₵12 respectively. Each product has to go through a manufacturing, assembly, and testing phase. The company’s resources are such that only 20 hours of manufacturing, 20 hours of assembly, and 20 hours of testing are available. Each unit of product 1 has to spend 1 hour in manufacturing, 2 hours in assembly, and 2 hours in testing. Each unit of product 2 has to spend 2 hours in manufacturing, 1 hour in assembly, and 2 hours in testing. Each unit of product 3 has to spend 2 hours in manufacturing, 2 hours in assembly, and 1 hour in testing. Company ABC wants to know how many units of each product it should produce, in order to maximize its profit.a) Formulate a linear programming model for this problem.
y = demand for the large bottle of Fresh in the sales period(Demand)x1 = the price of product 1x2 = the price of product 2x3 = the advertising expenditure for Freshx4 = the price difference in the sales periodAdver = types of advertising campaignsCampaign A consists entirely of television commercials, campaign B consists of a balancedmixture of television and radio commercials, and campaign C consists of a balanced mixture oftelevision, radio, newspaper, an dmagazine ads. To ultimately increase the demand for Fresh,Enterprise Industries’ marketing department is comparing the effectiveness of three differentadvertising campaigns. To compare the effectiveness of advertising campaigns A, B, and C, wedefine two dummy variables. Specifically, DB is 1 if campaign B is used and 0 otherwise, DC is1 if campaign C is used and 0 otherwise. Our proposed model is y = β0 + β1x4 + β2x3 + β3x 2 3 + β4x4x3 + β5DB + β6DC
A farmer has a 50-acre farm on which to plant pepper and tomatoes. The farmer has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres’ worth of pepper and 37 acres’ worth of tomatoes. An acre of pepper requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3 hours of labor and 20 tons of fertilizer. The profit from an acre of pepper is GH¢400, and the profit from an acre of tomatoes is GH¢300. The farmer wants to know the number of acres of pepper and tomatoes to plant to maximize profit. a). Formulate a linear programming model for this problem. b) i. Transform the model into a standard form ii. Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points. iii. Using the computer, determine the shadow prices for the resources and explain their meaning (show the sensitivity report).
kindly answer items (d) and (e)
A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: z = 100p-75,0.25 Chemical P costs $100 a unit and chemical R costs $700 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $112,000. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units

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