They want to maximize profit. Formulate alinear programming modelA refinery produces three grades (A, B, C) of gasolines from threedifferent sources of crude oil (I, II, III). Any crude oil can be used toproduce any of the gasolines as long as the specifications in thefollowing table are met.Grade of gasolineSpecificationsNot less than 50% crude I,not more than 30% crude IINot less than 35% crude I,Selling price/gallon$1.39$1.24not more than 45% crude IINot more than 20% crude IIIC$1.18The maximum amount of crude oil available per period and their costsareCrude I: 10,000 gallons, $1.10 cost/gallonCrude II: 9,000 gallons, $0.84 cost/gallonCrude III: 3,000 gallons, $0.90 cost/gallon

here, selling and cost price are given. The difference between both I.e. profit will be maximized.

Answered: They want to maximize profit. Formulate…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section: Chapter Questions

Problem 32P

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Another way to derive a demand function is to break the market into segments and identify a low price, a medium price, and a high price. For each of these prices and market segments, we ask company experts to estimate product demand. Then we use Excels trend curve fitting capabilities to fit a quadratic function that represents that segments demand function. Finally, we add the segment demand curves to derive an aggregate demand curve. Try this procedure for pricing a candy bar. Assume the candy bar costs 0.55 to produce. The company plans to charge between 1.10 and 1.50 for this candy bar. Its marketing department estimates the demands shown in the file P07_47.xlsx (in thousands) in the three regions of the country where the candy bar will be sold. What is the profit-maximizing price, assuming that the same price will be charged in all three regions?
This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.

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