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The following exercise gives you experience in using the cost and revenue functions to find the break-even point. (See Example 4.)

Austin Avenue Clothiers pays $53 each for sports coats and has a fixed monthly cost of $790. The store sells the coats for $74 each.
(a) What is the linear cost-volume function C(x)?
C(x) = 53x+790
Correct: Your answer is correct.


(b) What is the linear revenue function R(x)?
R(x) = 74x
Correct: Your answer is correct.


(c) What is the break-even number of coats? (Round your answer up to the nearest whole number.)
coats

The following exercise gives you experience in using the cost and revenue functions to find the breakeven point See Example 4 Austin Avenue Clothiers pays 53 ea class=

Respuesta :

Break even number of coats will be 38.

Given in the question,

  • Linear cost value function → C(x) = 53x + 790
  • Linear revenue function → R(x) = 74x

Linear profit function will be,

P(x) = R(x) - C(x)

And condition for the break even point → P(x) = 0

Therefore, P(x) = R(x) - C(x) = 0

By substituting the values of P(x) and R(x),

53x + 790 = 74x

74x - 53x = 790

21x = 790

x = 37.62

x ≈ 38

   Therefore, break even number of coats will be 38.

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