Answer :
Answer:
The total profit from producing 50 wedding cakes is 2,150 dollars
Step-by-step explanation:
Stevens Bakery has found that its marginal profit, in dollars per wedding cake, is [tex]C'(x) = - 0.12 x + 40[/tex] , where x is the number of wedding cakes produced
From the given information:
C'(x) = - 0.12 x + 40
Integrate both sides we get,
[tex]\int C'(x) dx = \int (-0.12x+40)dx[/tex] [tex]\int x^n dx = \frac{x^{n+1}}{n+1}+C[/tex]
[tex]C(x) = -0.12 \times \frac{x^{2}}{2}+40x[/tex]
[tex]C(x) = -0.06x^2+40x[/tex] ...... (1)
Substitute the value of x=50 wedding cakes in equation (1) as shown below:
[tex]C(50) = -0.06 (50)^2 +40(50) = 150+2000[/tex]
=2,150 dollars
Hence, the total profit from producing 50 wedding cakes is 2,150 dollars.
Answer:
2150 Profit at 50 cakes quantity
Step-by-step explanation:
Marginal Profit [C'(x)] is Addition to total profit due to increase in quantity 'x'. So it is derivation of 'total profit function' with respect to 'quantity x'= ∂TP/∂x. Hence, Total Profit is integration of Marginal Profit with respect to x.
Marginal Profit : C'(x) = -0.12x + 40
Total Profit : C (x) = ∫-0.12x + 40
= -0.12x^2 / 2 + 40x
Total Profit Function = 0.06x^2 + 40x
Total Profit at given quantity = 50 cakes :
0.06 (50)^2 + 40 (50)
0.06 (2500) + 2000
150 + 2000
= 2150 [ Profit at 50 cakes quantity ]