What price should the units be sold for a revenue of 10450?

Question

A company sells 4000 units each for \$2. For every 5 cent increase, 40 fewer are sold. At what price should they sell if they want a revenue of \$10450?

Answer 1

Model your equation using a quadratic function:

$(4000-40x)(2+0.05x)=y$

This is true because price is given by the second bracket and the units is given by the first bracket.

Now solve for $x$ by plugging in $y=10450$

Then your price is given by $2+0.05x$

Answer 2

HINT

The demand seems like a linear function of the price, so $D(p) = mp+b$.

• Find $m$ from the description of the change in demand when you change prices.
• Find $b$ from the point $(2, 4000)$ that you are given.
• Revenue is price times units sold, i.e. $R(p) = p D(p)$. Use $D(p)$ you found to express what equation will $R(p)$ obey
• Can you solve $R(p) = 10450$?