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Question 1083835: Baskets inc is planning to introduce a new basket to their company. The company estimates that $500 worth of new equipment will be needed to manufacture the new type of basket and it will cost $15 to make each basket. The company also estimates that the revenue from each basket will be $31.
A) Determine the revenue function R (x) from the sale of x baskets.
B) Determine the cost function C (x) for manufacturing x baskets.
C) Find the break-even point. Round to the nearest whole basket.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! R = 31 * x
R is the revenue
x is the number of baskets sold.
C = 500 + 15 * x
C is the cost of production.
x is the number of baskets produced.
the break even point is when R = C
this occurs when 31 * x = 500 + 15 * x
subtract 15 * x from both sides to get 16 * x = 500
divide both sides by 16 to get x = 500 / 16 = 31.25
the break even point is between 31 and 32 baskets.
when 31 baskets are produced and sold, the revenue is 31 * 31 = 961 and the cost is 500 + 15 * 31 = 965.
when 32 baskets are produced and sold, the revenue is 32 * 31 = 992 and the cost is 500 + 15 * 32 = 980.
if you round to the nearest integer, then the solution would be 31 baskets is the break even point.
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