Question

The profit, in dollars, of a small business can be modeled by the function P(x)=0.3x^2+7x-40, where c is the number of units sold. How many units need to be sold for the business to make a profit of 60$?

Answer 1

The correct answer is 10 units.

Explanation:

Profit function of a small business is given by P(x) = 0.3
`x^(2)` + 7x - 40, where x is the number of units sold.

The small business intend to make a profit of $60.

To find out the number of units the business has to sell in order to have a profit of $60 is given by,

P(x) = 0.3
`x^(2)` + 7x - 40 = 60

⇒ 0.3
`x^(2)` + 7x - 100 = 0

⇒ 3
`x^(2)` + 70x - 1000 = 0

⇒ x = -70 ±
`\sqrt{(70)^(2) + 12000}` ×
`(1)/(6)`

⇒ x = -70 ± 130 ×
`(1)/(6)`

⇒ x = 10 or -
`(200)/(6)`

Quantity sold cannot be negative giving us the value of x as 10 units.