The average profit in dollars A that your baking business makes when baking n cakes is given by . Find and explain the vertex.
A) If you make 44 cakes you maximize your profit at $484.
B) If you make 44 cakes you minimize your profit at $484.
C) If you make 88 cakes you make no profit.

Question

The average profit in dollars A that your baking business makes when baking n cakes is given by  . Find and explain the vertex.
A) If you make 44 cakes you maximize your profit at $484. 
B) If you make 44 cakes you minimize your profit at $484. 
C) If you make 88 cakes you make no profit.

Quizplus · Accepted Answer

The vertex of the quadratic function represents the maximum or minimum point of the function. In this case, the quadratic function given is A(n) = -0.5n^2 + 33n, where n represents the number of cakes baked. The coefficient of the n^2 term is negative, indicating that the graph is a downward-facing parabola, which means that the vertex represents the maximum point of the function.

To find the vertex, we can use the vertex formula:
n = -b / 2a, where a = -0.5 and b = 33.
n = -33 / 2(-0.5) = 33 / 1 = 33

Substituting n = 33 into the A(n) function gives:
A(33) = -0.5(33)^2 + 33(33) = 544.5

Therefore, the maximum profit of $544.50 is attained when 33 cakes are baked. However, since the number of cakes must be a whole number, we round up to 44 cakes. Thus, the best choice is to bake 44 cakes.

The Average Profit in Dollars a That Your Baking Business