no name asked in 科學及數學數學 · 10 years ago

help!!!Maths(cost)

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?

1 Answer

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  • 10 years ago
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    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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