The total revenue that is gained from the sales of the cakes is determined by multiplying the number of cakes by the price. If we let x be the number of $1 that should be deducted from the price and y be the total revenue, y = (25 - x)(100 + 5x)Simplifying, y = 2500 + 25x - 5x²We get the value of x that will give us the maximum revenue by differentiating the equation and equating the differential to zero. dy/dx = 0 = 25 - 10xThe value of x is 2.5. The price of the cake should be 25 - 2.5 = 22.5. Thus, the price of the cake that will give the maximum potential revenue is $22.5
Answer:
Step-by-step explanation:
x^2 - 22x = 10
Next step is to complete the square on the left hand side of the equation and it would be balanced by adding the same number to the right side of the equation. It becomes
x^2 - 22x + (22/2)^2 = 10 + (22/2)^2
x^2 - 22x + (11)^2 = 10 + (11)^2
x^2 - 22x + (11)^2 = 10 + 121
x^2 - 22x + (11)^2 = 131
x^2 - 22x + 121^2 = 131
(x - 11)^2 = 131
Taking square root of both the left hand side and the right hand side of the equation, it becomes
x - 11 = ±√131
x - 11 = ±11.45
Adding 11 to the left hand side and the right hand side of the equation, it becomes
x - 11 + 11 = ±11.45 + 11
x = 11.45 + 11 or x = -11.45 + 11
x = 22.45 or x = - 0.45
<span>.12x + .08(45000-x)
</span>.12x + 3600 - .08x
.12x - .08x + 3600
.04x + 3600
combined yearly interest = .04x + 3600