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

Question

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

Answer 1

The equation is a quadratic with 

y-values representing the cost

and x-values representing the

number of cakes

 

The x-value for your vertex point

would be the minimum number of 

cakes yielding the minimum cost y

 

Your graph opens up and does not 

cross the x-axis, no x-intercepts

 

Let's change the equation to graphing

form and that will show you the vertex:

 

       y = .5X² - 12X + 150

 

Complete the square with the X's

 

      Y = .5 (X - 6 )²  + 150 - 18

 

Completing the square added 18 ( .5 times 36 ) to the right side,

so we had to subtract 18 in order not to change the value of the

equation

 

      Y = .5 (X - 6)² + 132

 

The vertex for the parabola is (6 , 132)

 

6 cakes will cost $132 to make, this is the minimum