A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $18,000, and the monthly fixed costs of using Machine II are $15,000. The variable costs of manufacturing 1 unit of the product using Machine I is $15, and the variable costs of manufacturing 1 unit of the product using Machine II is $20. The product sells for $50 per unit. Find the cost function associated with manufacturing on each machine.Find the profit function associated with manufacturing on each machine.Which machine would be preferred if sales estimates indicate that we could sell 450 units? Which would be preferred if we could sell 650 units?

Let x be the number of machines sold For Machine I The monthly fixed costs of using Machine I are $18,000The variable costs of manufacturing 1 unit of the product using Machine I is $15 ⇒C1x=18000+15x For Machine II The monthly fixed costs of using Machine II are $15,000The variable costs of manufacturing 1 unit of the product using Machine II is $20 ⇒C2x=15000+20xRevenue function The product sells for $50 per unit⇒Rx=50x Profit function for Machine 1 ⇒P1x=Rx-C1x⇒P1x=50x-18000+15x⇒P1x=35x-18000 Profit function for Machine II ⇒P2x=Rx-C2x⇒P2x=50x-15000+20x⇒P1x=30x-15000At x=450 units ⇒P1450=35450-18000=-2250⇒P2450=30450-15000=-1500 At x=650 units ⇒P1650=35650-18000=4750⇒P2450=30650-15000=4500Hence a) Cost function of Machine 1 C1(x)=18000+15x Cost function of Machine II C2(x)=15000+20x b) Profit function of Machine IP1(x)=35x-18000 Profit function of Machine IIP2(x)=30x-15000 c) If company sell 450 units then they need to sell Machine II because it contain less loss i.e. 1500 compare to Machine I loss 2250 If company sell 650 units then they need to sell Machine I because it containMore profit i.e. 4750 compare to Machine II profit i.e. 4500

Answered: A product may be made using Machine I…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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A product may be made using Machine I or Machine II. The manufacturer estimates that the monthly fixed costs of using Machine I are $18,000, and the monthly fixed costs of using Machine II are $15,000. The variable costs of manufacturing 1 unit of the product using Machine I is $15, and the variable costs of manufacturing 1 unit of the product using Machine II is $20. The product sells for $50 per unit.

Find the cost function associated with manufacturing on each machine.

Find the profit function associated with manufacturing on each machine.

Which machine would be preferred if sales estimates indicate that we could sell 450 units? Which would be preferred if we could sell 650 units?

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