To produce x units of a religious medal costs

Question

To produce x units of a religious medal costs C(x)= 18x+63. The Revenue is R(x)= 27x. Both cost and revenue are in dollars.

a.Find the? break-even quantity.
b. Find the profit from 470 units.
c. Find the number of units that must be produced for a profit of ?$90

Answer 1

The break-even quantity is the intersection of the cost and revenue lines.

 

The profit is the difference between revenue and cost.

 

 

C(x) = 18x + 63

 

R(x) = 27x

 

The break-even point is where C(x) = R(x).

 

18x + 63 = 27x

 

63 = 9x

 

x = 7.  (a)

 

Seven units must be produced (and sold) to break even.  Breaking even is recovering start-up costs like money borrowed from mom to start the business.

 

 

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

 

P(x) = 27x - (18x + 63)

 

P(x) = 27x - 18x - 63

 

P(x) = 9x - 63

 

 

P(470) = 9(470) - 63

 

P(470) = 4167

 

The profit on 470 units is $4,167.  (b)

 

 

The number of units to yield a profit of $90 comes by solving P(x) for x when P(x) = 90.

 

P(x) = 9x - 63 = 90.  Solve for x.

 

9x - 63 = 90

 

9x = 27

 

x = 3.

 

 

Three units must be produced (and sold) to generate $90 of profit.