Kristen owns a bakery called Kristen’s cakes and such and is considering lowering the price of her cakes Kristen pulls her customers and determines that she can sell 100 cakes each week when she charges $25 each she also discovers that for every one dollar decrease in the price of the cake she will sell five more cakes the graph below represents Christians projected weekly revenue for each decrease in the price at what price she Christian sell her cakes in order to meet her maximum potential revenue
Accepted Solution
A:
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