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A baker has modeled the monthly operating costs for making wedding cakes by the function y=0.5x^2 - 12x + 150, where the monthly operating costs in dollars and x is the number of cakes prepared.

AWhat is the minimum cost?

BHow many cakes should be prepared each month to yield the minimum cost?

Verified Answer :

DavidBWA21

The minimum cost y = $78. 

 
x = 12 cakes to yield minimum cost.

sandie1984

1)
y = 0.5x^2 - 12x + 150
axis of symmetry x = -b/(2a)
x = 12/1 = 12

y = 0.5(x^2 - 24x + 144) - 72 + 150
y = 0.5(x - 12)^2 + 78
vertex = (12, 78)

2)
The vertex is the minimum point, and the minimum cost y = $78.

3)
x = 12 cakes to yield minimum cost.

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