Answer :
Answer:
The two values of x are 20 and 60
Step-by-step explanation:
Given;
cost function: C = 60x + 300
revenue function: R = 100x − 0.5x²
Profit = R - C
300 = 100x − 0.5x² - ( 60x + 300)
300 = 100x − 0.5x² - 60x - 300
300 + 300 = 100x − 0.5x² - 60x
600 = 40x - 0.5x²
600 = 40x - ¹/₂x²
multiply both sides by 2
1200 = 80x - x²
re-write the equation
80x - x² = 1200
-x² + 80x - 1200 = 0
multiply through by (-1)
x² - 80x + 1200 = 0
factorize the quadratic equation
x² (- 60x - 20x) + 1200 = 0
x² - 60x - 20x + 1200 = 0
x(x - 60) -20(x - 60) = 0
(x - 20)(x - 60) = 0
x - 20 = 0 or x - 60 = 0
x = 20 or 60
Therefore, the two values of x are 20 and 60
The values of x that would give a profit of $300 is 20 and 60.
Revenue is the total amount of money that can be made from selling x items while cost is the amount of money used to produce x items.
Profit is the difference between revenue and cost. Profit is given by:
Profit = Revenue - Cost
Since Cost C = 60x + 300, Revenue R = 100x − 0.5x², hence:
Profit = Revenue - Cost
Profit = 100x − 0.5x² - (60x + 300)
Profit = 40x - 0.5x² - 300
For a profit of $300:
300 = 40x - 0.5x² - 300
0.5x² - 40x + 600 = 0
x = 20 and x = 60
Hence the values of x that would give a profit of $300 is 20 and 60.
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