Mrs. G likes to make and sell posters. The function graphed to the left indicates how much profit she makes in a month if she sells the posters for 20 - x dollars each.
10. What should Mrs. G charge per poster to make the maximum profit?
11. What is that profit?
To find the price per poster that will maximize Mrs. G's profit, we need to locate the peak point on the graph. The x-coordinate of this point will represent the price per poster.
To determine the maximum profit, we need to find the corresponding y-coordinate of the peak point, which will indicate the profit Mrs. G will make.
Here's how we can find the answers to both questions:
10. To determine the price per poster that maximizes profit, we need to find the x-coordinate of the peak point on the graph. This can be done by identifying the highest point on the graph. If you have a visual representation of the graph, locate the highest point on the curve. This point's x-coordinate will represent the price per poster that maximizes profit.
If you only have the equation of the graph, you can find the x-coordinate of the peak point by setting the derivative of the equation equal to 0 and solving for x. The resulting value of x will be the price per poster that maximizes profit.
11. Once you have identified the x-coordinate of the peak point, substitute this value into the equation provided to find the corresponding y-coordinate. This y-coordinate will represent the maximum profit Mrs. G can make.
By finding the x-coordinate that maximizes profit, you can answer question 10 and by substituting this value into the equation, you can answer question 11.