Answer:
10 units need to be sold for the business to make a profit of $60
Step-by-step explanation:
The profit, in dollars, of a small business can be modeled by the function
P(x) = 0.3 x² + 7x - 40, where x is the number of units sold
∵ The profit is $60
- That means substitute P(x) by 60
∴ P(x) = 60
- Equate 0.3 x² + 7x - 40 by 60
∵ 0.3 x² + 7x - 40 = 60
- Subtract 60 from both sides
∴ 0.3 x² + 7x - 100 = 0
- Multiply both sides by 10
∴ 3x² + 70x - 1000 = 0
Now let us factorize the left hand side into two factors and equate each factor by 0 to find x
∵ 3x² = (3x)(x)
∵ -1000 = (100)(-10)
∵ (3x)(-10) + (x)(100) = -30x + 100x = 70x
- That means the factors are (3x + 100) and (x - 10)
∴ The factors of 3x² + 70x - 1000 are (3x + 100) and (x - 10)
∴ (3x + 100)(x - 10) = 0
Equate each factor by 0
∵ 3x + 100 = 0
- Subtract 100 from both sides
∴ 3x = - 100
- Divide both sides by 3
∴ x = [tex]-\frac{100}{3}[/tex]
We will refused this answer because number of units sold must be positive integer
∵ x - 10 = 0
- Add 10 to both sides
∴ x = 10
10 units need to be sold for the business to make a profit of $60
