Cost revenue and profit function-
A firm sales a single product for $ \$ 65$ per unit. The variable cost are $ \$20$ for material and $ \$27.50$ for labour. Annual fixed cost are $\$100000$.
A.) Construct the profit stated in terms of "$x$", where $x$ represents the number of units produced and sold.
B.) What profit is earned if annual sale is $20000$ units?
Assuming that the number of units produced and sold is the same, profit $\pi$ can be expressed as: $$ \pi(x)=\text{Revenue} - \text{Expenses} = 65x-[(20+27.5)x +100,000] = 17.5x-100,000 $$ If $x=200,000$ units per year, then $\pi=\$250,000$ per year.