Question

Toy Universe is manufacturing a new toy and deciding on a price that will result in a maximum profit. The graph below represents profit (P) generated y each price of a toy (x).

**Graph is attached below (sorry the picture is bad quality)**

Part A: If the company wants to make a maximum profit, what should the price of a new toy be?

Part B: What is the minimum price of a toy that will produce profit for the company? Explain your answer.

Part C: Estimate the value of P(10) and explain what the value means in the problem and how this may be possible.

Part D: If the company wants to make a profit of $137, for how much should the toy be sold.

Part E:Find the domain that will only result in a profit for the company and find its corresponding range of profit.

Part F: The company owner believes that selling the toy at a higher price will result in a greater profit . Explain to the owner how selling the toy at a higher price will affect the profit.

Answer 1

To maximize profit, find the highest point on the profit graph. The minimum price that will produce profit can be found by determining the lowest point on the graph. To estimate P(10), find the corresponding profit value on the graph. To make a profit of $137, find the price either by using the graph or solving the profit equation. The domain for profit can be found by determining where profit is greater than or equal to zero. Selling at a higher price can result in higher profit, but there is an optimal price range.

Step-by-step explanation:

In order to find the price that will result in maximum profit for Toy Universe, we need to find the highest point on the profit graph. This price will correspond to the X-coordinate of the vertex of the profit graph.

If the graph is not available, we can calculate the price by finding the value of x where the derivative of profit with respect to price is zero.

To find the minimum price that will produce profit for the company, we need to determine the lowest point on the profit graph. This price will correspond to the X-coordinate of the lowest point on the graph.

To estimate the value of P(10), we can find the corresponding profit value for a price of 10 on the graph. This will give us an approximate idea of the profit at that price.

To find the price at which the company can make a profit of $137, we can either use the graph to find the corresponding price or calculate it by solving the profit equation for the given profit value.

The domain that will only result in a profit for the company can be found by determining the range of x-values on the profit graph where the profit is greater than or equal to zero. The corresponding range of profit will be the set of y-values where the profit is greater than or equal to zero.

If the company believes that selling the toy at a higher price will result in a greater profit, it is likely because the graph of profit vs. price shows that the profit increases as the price increases. This means that as long as the price is within a certain range, increasing the price will result in a higher profit. However, it is important to note that if the price becomes too high, the profit will start to decrease as demand decreases.

Answer 2

A: $6

B: $2.01

C: $0

D: $4.50 or $7.50

E: 0 ≤ x ≥ 10

F: The more expensive you make the toy then that will mean that less people will want to buy it for its high price.

Step-by-step explanation:

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