Question

NO LINKS!!! URGENT HELP PLEASE!!!!

The amount of profit (in millions) made by Scandal Math, a company that writes math problems based on tabloid articles, can be found by the equation P(n) = -n^2 + 10n, where n is the number of text sold (also in millions). Find the maximum profit and the number of textbooks that Scandal Math must sell to realize the maximum profit. HINT: This is a parabola. . . find the maximum value of the graph

Answer 1

$25 million

Explanation:

The profit function given is a quadratic equation with a negative coefficient for the squared term, which means that the graph of this function is a downward-opening parabola. The maximum profit will be at the vertex of this parabola, which occurs when n = -b/2a, where a and b are the coefficients of the squared and linear terms, respectively.

In this case, a = -1 and b = 10, so the number of textbooks sold to realize the maximum profit is given by:

n = -b/2a = -10/(2*(-1)) = 5

To find the maximum profit, we can plug this value of n into the profit function:

P(5) = -(5)^2 + 10(5) = -25 + 50 = 25

the maximum profit that Scandal Math can make is $25 million, and this occurs when they sell 5 million textbooks.

Answer 2

The maximum profit the company can make is $25 million and they must sell 5 million textbooks to realise the maximum profit.

Explanation:

Given equation:

`P(n) = -n^2 + 10n`

where:

• P(n) is the profit made (in millions).
• n is the number of textbooks sold (in millions).

The given equation is a quadratic function. Therefore, the graph of the function is a parabola. Since the leading coefficient of the equation is negative, the parabola opens downwards.

The maximum profit and the number of textbooks Scandal Math must sell to realize the maximum profit is represented by the vertex of the parabola.

The x-value of the vertex can be found using the formula -b/2a for a quadratic in the form ax² + bx + c.

The values of a and b for the given quadratic function are:

• a = -1
• b = 10

Substitute these values into the formula to find the x-value of the vertex:

`\implies x=-(b)/(2a)=-(10)/(2(-1))=-(10)/(-2)=5`

To find the y-value of the vertex, substitute x = 5 into the function:

`\begin{aligned}x=5 \implies P(5)&=-(5)^2+10(5)\\&=-25+50\\&=25\end{aligned}`

Therefore, the vertex of the parabola is (5, 25).

This means that the maximum profit the company can make is $25 million and they must sell 5 million textbooks to realise the maximum profit.