Question

What’s the function representing the total daily profit, P(x), after selling x units

Answer 1

Profit can be calculated by subtracting the total cost from the total revenue.

We have the equations for Revenue and Cost, so we can calculate the profit as follows:

Profit = Revenue - Cost


`=-0.32 x^(2) +270x-(70x+52) \\ \\ =-0.32 x^(2) +270x-70x-52 \\ \\ =-0.32 x^(2)+200x-52`

The equation shown above gives the profit in terms of x number units. By replacing x with the number of units, for which we want to calculate the profit, we can directly find the profit.

Answer 2

The function that represents the total daily benefit, P (x), after selling x units is the difference of R (x) -C (x)
That is to say:
P (x) = -0.32x ^ 2 + 270x - (70x +52)
P (x) = -0.32x ^ 2 + 270x -70x -52
P (x) = -0.32x ^ 2 + 200x -52
Finally, the function that represents the total daily benefit C is:
P (x) = -0.32x ^ 2 + 200x -52