P = 105x − 100 − x2,
what level(s) of production will yield a profit of $2350?
To find the level(s) of production that will yield a profit of $2350, we can set the profit function equal to $2350 and solve for x.
Given: P = 105x - 100 - x^2
Profit = $2350
Setting up the equation:
2350 = 105x - 100 - x^2
Rearranging the equation to standard form:
x^2 - 105x + 2450 = 0
Now we can solve this quadratic equation to find the values of x that satisfy the condition.
Using factoring or quadratic formula, we find the roots of the equation are:
x = 35 and x = 70
Therefore, the level(s) of production that will yield a profit of $2350 are x = 35 and x = 70.
To find the level(s) of production that will yield a profit of $2350, we can set the profit function equal to $2350 and solve for x.
Profit function: P = 105x - 100 - x^2
Setting the profit function equal to $2350:
2350 = 105x - 100 - x^2
Rearranging the equation:
x^2 - 105x + 2450 = 0
To solve this quadratic equation, you can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our case, a = 1, b = -105, and c = 2450. Plugging these values into the quadratic formula:
x = (-(-105) ± √((-105)^2 - 4(1)(2450))) / (2(1))
Simplifying further:
x = (105 ± √(11025 - 9800)) / 2
x = (105 ± √(1225)) / 2
x = (105 ± 35) / 2
Solving for both possible values of x:
1. x = (105 + 35) / 2 = 140 / 2 = 70
2. x = (105 - 35) / 2 = 70 / 2 = 35
So, the level(s) of production that will yield a profit of $2350 are x = 70 and x = 35.
just solve
2350 = 105x - 100 - x^2
x^2 - 105x + 2250 = 0
(x-35)(x-70) = 0