Chart II.ConstraintDual ValueSlack/SurplusOriginal ValLower BoundUpper BoundInifinity9750012000Vat Capacity14189.192700012810.81Grain0.64864874500042000Premium70005000-InfinityPremium/Light0.729729712000500012857.14 A local brewery produces three types of beer: premium, regular and light. The brewery hasenough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beerrequires 3.5 pounds of grain, a gallon of regular requires 3.7 pounds of grain, and a gallon oflight requires 4.2 pounds of grain. The brewery is able to acquire 45,000 pounds of grain everymonth. While the brewery's largest seller is regular beer, it wants to have a competitive marketmix of beer. Thus, the brewery wishes to produce at least 5,000 gallons of premium beer, but notmore than 12,000 gallons of light and premium beer combined. The brewery makes a profit of$3 per gallon of premium beer, $2.40 per gallon of regular beer, and $2.80 per gallon of lightbeer. The brewery manager wants to know how much of each type of beer should be producedin order to maximize profit. Use the following model and accompanying POM printout toanswer the following questions.Note:Xi = gallons of premiumX2 = gallons of regularX3 = gallons of lightmaximize Z = $Зх1 + 2.40х2 + 2.80х3Subject to:X1 + x2 + X33.5x1 + 3.7x2 ± 4.2x3< 27,000 (1) vat capacity< 45,000 (2) Grain2 5,000 (3) premium< 12,000 (5) combined premium/light> 0X1X1 + X3X1, X2, XзChart I.VariableValueReduced CostOriginal ValLower BoundUpper BoundPremium X12.35Infinity120003Regular X2Light X3810.812.43.170.652.8-Infinity3.45

Problem is Max Z = 3 x1 + 2.4 x2 + 2.8 x3 subject to x1 + x2 + x3 ≤…

A local brewery produces three types of beer: premium, regular and light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 3.5 pounds of grain, a gallon of regular requires 3.7 pounds of grain, and a gallon of light requires 4.2 pounds of grain. The brewery is able to acquire 45,000 pounds of grain every month. While the brewery's largest seller is regular beer, it wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 5,000 gallons of premium beer, but n more than 12,000 gallons of light and premium beer combined. The brewery makes a profit of $3 per gallon of premium beer, $2.40 per gallon of regular beer, and $2.80 per gallon of light beer. The brewery manager wants to know how much of each type of beer should be produced in order to maximize profit. Use the following model and accompanying POM printout to answer the following questions.

A local brewery produces three types of beer: premium, regular and light. The brewery has enough vat capacity to produce 27,000 gallons of beer per month. A gallon of premium beer requires 3.5 pounds of grain, a gallon of regular requires 3.7 pounds of grain, and a gallon of light requires 4.2 pounds of grain. The brewery is able to acquire 45,000 pounds of grain every month. While the brewery's largest seller is regular beer, it wants to have a competitive market mix of beer. Thus, the brewery wishes to produce at least 5,000 gallons of premium beer, but n more than 12,000 gallons of light and premium beer combined. The brewery makes a profit of $3 per gallon of premium beer, $2.40 per gallon of regular beer, and $2.80 per gallon of light beer. The brewery manager wants to know how much of each type of beer should be produced in order to maximize profit. Use the following model and accompanying POM printout to answer the following questions.

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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