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?