help!!!Maths(cost)

2010-03-09 2:19 am
A factory manufactures pens, the fixed cost of $20000, and the variable costs are $2.30 materials, $3.00 labour, and $0.70 overhead per each pen. Let x represent the number of pens produced and sold. The selling price is $10 for each pen.

a) Express the cost function C(x) and the profit function P(x) in terms of x.
b) Producing how many pens will result in break-even?
c) How many pens must be produced to make a profit of $5000?

回答 (1)

2010-03-09 2:27 am
✔ 最佳答案
a)

C(x) = 20,000 + (2.30 + 3.00 + 0.70)x

P(x) = 10x - C(x)
P(x) = 10x - (20,000 + (2.30 + 3.00 + 0.70)x)

b)

P(x) = 0
10x - (20,000 + (2.30 + 3.00 + 0.70)x) = 0
10x = 20,000 + 6x
x = 5,000

c)

P(x) = 5,000
10x - (20,000 + (2.30 + 3.00 + 0.70)x) = 5,000
10x = 25,000 + 6x
x = 6,250


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