If = 3x + 20 and = 44 – 5x  where x is the number of units produced and sold, and the cost of production of 80 units is $11,400, find the total cost and the total revenue functions. b) Find the profit (or loss) at this level. At what value of  x  is the profit maximized.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
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ISBN:9780079039897
Author:Carter
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Chapter3: Linear And Nonlinear Functions
Section3.2: Zeros Of Linear Fumctions
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If = 3x + 20 and = 44 – 5x  where x is the number of units produced and sold, and the cost of production of 80 units is $11,400, find the total cost and the total revenue functions.

b) Find the profit (or loss) at this level. At what value of  x  is the profit maximized.

Expert Solution
Step 1

 

We know that

Marginal cost =dC(x)dx= 3x + 20

C(x)=3x+20dx

 

Marginal revenue =dR(x)dx=  44 – 5x

R(x)=44-5xdx

 the cost of production of 80 units is $11,400

Step 2

Calculus homework question answer, step 2, image 1

Total Cost function C(x)=32x2+20x+200

Total Revenue function R(x)=44x-52x2

Profit function P(x)=24x-4x2-200

 

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