Question

A business owner used a revenue function and a cost function to analyze his monthly sales. One month he found that with a sales volume of 600 items he had revenues of $54,000. Another month he had total costs of $20,800 on a sales volume of 400 items. He also finds that the break-even point is 20 items.

(a) Find the revenue function. (I solved this part of the question).
(b) Find the cost function. (I need help with this question).

Answer 1

Revenue Function = 90x

cost function = 50x + 800

Step-by-step explanation:

given data

sales volume = 600 items

revenues = $54,000

total costs = $20,800

sales volume = 400 items

break-even point = 20 items

solution

first we get here Price per unit for Revenue Function that is express as

Price per unit =
`(total\ sale)/(no\ of unit)`

Price per unit =
`(54000)/(600)`

Price per unit = $90

so here Revenue Function will be

Revenue Function = 90x .......................1

here x is sale volume

and

cost function will be

cost function = ax +b .........................2

here

a is Variable cost per unit and b is fixed cost and x is sale function

so when cost at 400 units will be

$20800 = 400a + b .......................3

and

Cost at break even point will be

$90 × 20 = 20a + b ..........................4

as here total cost = total revenue

so from equation 3 and 4 we get a and b

380a = $19000

a = $50

and

b = $20800 - 400 × 50

b = $800

so here Cost Function will be from equation 2

cost function = 50x + 800