Q1) A company sells a product for $150 per unit. Raw material cost are $40 per unit,
labor costs are $55 per unit, shipping costs are $15 per unit, and the annual fixed costs are $200,000. (6) a) Determine the profit functionP = f(x), where x equals the number of units sold. b) How many units must be sold in order to break even? c) What profit is earned if annual sales are 20,000 units?
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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