[Math] determine the revenue, cost and profit functions

calculus

The demand of gloves is $$x(p)=20,000-2000p,$$ where p denotes price per pair. The total cost of $x$ pairs of gloves is $$c(x)=30,000+1.50x$$ dollars.

  1. Determine the revenue and cost functions in terms of price $p$.
  2. Determine the price range that will earn maximum profit.
  3. Determine the break even point.

Best Answer

  1. $$r(p) = p\cdot d(p)$$ $$ c(x(p))= 30,000+1.50(20,000-2000p)$$
  2. For profit function π, $$π=r(p)-c(p)$$ To maximize profit, set $$π'(p)=r'(p)-c'(p)=0$$
  3. Break even when revenue = cost. Solve for $p$ in the following equation: $$r(p)=c(p)$$
Related Question