The answers are
- A. The equation for the profit from selling the items is P = 40x-0.5x²-300.
- b. The values of x are 10 and 70.
- c. It is not possible to have the profit of 2500
<h3>How to solve for the expression</h3>
We have the cost function in this question to be
C(x) = 60x+300
We have the function of the revenue to be
Revenue = 100x−0.5x²
A. The formula for revenue function is given
revenue - cost
This is expressed as
= (100x−0.5x²)-60x+300
We have to collect like terms and open the equation above.
This given us:
<h3>40x-0.5x²-300</h3>
B. when profit = 50$
We have p = 40x-0.5x²-300
50 = 40x-0.5x²-300
Multiply the two sides by 10
This gives
500 = 400x - 5x² - 3000
This gives a quadratic equation
5x² - 400x - 3500 = 0
To solve the equation you have to make use of a quadratic calculator.
This gives us the values
<h3>x = 10</h3><h3>x = 70</h3>
c. We have P = 40x-0.5x²-300.
at P = 2500
2500 = 40x-0.5x²-300.
Multiply the equation by 10
25000 = 400x - 5x² - 3000
collect like terms
400x - 5x2 - 3000 +28000
400x -5x2 +28000
We have to take the discriminant
-400² - 4*5*28000
= -400000
The discriminant is negative hence it is not possible.
Read more on quadratic polynomials here:
brainly.com/question/25841119
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