Answer:
The correct answer is 10 units.
Step-by-step explanation:
Profit function of a small business is given by P(x) = 0.3[tex]x^{2}[/tex] + 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[tex]x^{2}[/tex] + 7x - 40 = 60
⇒ 0.3[tex]x^{2}[/tex] + 7x - 100 = 0
⇒ 3[tex]x^{2}[/tex] + 70x - 1000 = 0
⇒ x = -70 ± [tex]\sqrt{(70)^{2} + 12000}[/tex] × [tex]\frac{1}{6}[/tex]
⇒ x = -70 ± 130 × [tex]\frac{1}{6}[/tex]
⇒ x = 10 or -[tex]\frac{200}{6}[/tex]
Quantity sold cannot be negative giving us the value of x as 10 units.
