The demand equation for a certain product is $\mathrm { P } = 75 - 0.001 \mathrm { x }$, where $\mathrm { x }$ is the number of units sold per week and $\mathrm { P }$ is the price in dollars at which one is sold. The weekly revenue $R$ is given by $R = x P$. What number of units sold produces a weekly revenue of $\$ 60,000$ ?
A) 74,191 units
B) 59,925,000 units
C) 792 units
D) 809 units

Question

Quizplus · Accepted Answer

To find the number of units sold that produces a weekly revenue of $60,000, we substitute $P = 75 - 0.001x$ into $R = xP$ to get $R = x(75 - 0.001x)$. Setting $R = 60,000$, we have $60,000 = x(75 - 0.001x)$. Solving this quadratic equation for $x$ yields the correct number of units, which is 809 units.

The Demand Equation for a Certain Product Is P=75−0.001x\mathrm { P } = 75 - 0.001 \mathrm { x }P=75−0.001x

The Demand Equation for a Certain Product Is $\mathrm { P } = 75 - 0.001 \mathrm { x }$