A company sells a product for $150 per unit. Raw material costs are $40 per unit, labor costs are $55 per unit, shipping costs are $15 per unit, and annual fixed costs are $200,000. a) determine the profit function P=f(x), where x equals the number of units sold. b) how many units must be sold in order to earn an annual profit of $750,000?
Answers
Given : A company sells a product for $150 per unit.
Raw material costs are $40 per unit,
labor costs are $55 per unit,
shipping costs are $15 per unit,
annual fixed costs are $200,000.
To find :
a) determine the profit function P=f(x), where x equals the number of units sold.
b) how many units must be sold in order to earn an annual profit of $750,000?
Solution:
Total cost function C(x) = Fixed costs + Variable costs
C(x) = 200,000 + 40x + 55x + 15x
=> C(x) = 200,000 + 110x
Revenue function R(x) = Selling Price * units
=> R(x) = 150x
profit function P=f(x) = R(x) - C(x)
= 150x - ( 200,000 + 110x )
= 40x - 200,000
profit function P=f(x) = 40x - 200,000
Units must be sold in order to earn an annual profit of $750,000
40x - 200,000 = 750,000
=> 40x = 950,000
=> x = 23750
23750 units must be sold in order to earn an annual profit of $750,000
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