A company distributes college logo sweatshirts and sells them for $55 each. The total cost function is linear, and the total cost for 50 sweatshirts is $4346, whereas the total cost for 240 sweatshirts is $7576. (a) Write the equation for the revenue function R (x).

Question

Business

Esther Rhodes

20 May, 16:14

A company distributes college logo sweatshirts and sells them for $55 each. The total cost function is linear, and the total cost for 50 sweatshirts is $4346, whereas the total cost for 240 sweatshirts is $7576. (a) Write the equation for the revenue function R (x).

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Answers (1)

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Mooney · Answer 1

The revenue equation is TR=55*P

Total cost equation is TC=3496+17Q

Explanation:

The formula for revenue is given quantity multiplied by price

TR=PQ

P is the price per unit ]

Q is the total quantity

since P is $55

TR=55P

The total cost function can also be determined thus:

TC = a+bQ

where a is the fixed cost

b is variable cost per unit

Q is the number of output

when TC is $4346, Q was 50

when TC was $7576 Q was 240

7576=a+240b

4346=a+50b

subtracting the two equations

3230 = 190b

b=3230/190

b=$17

by substituting b in any of the equations, fixed cost can be determined

4346=a + (17*50)

4346=a+850

a=4346-850

a=3496

Total cost function

TC=3496+17Q