Question 193256
the sound sleeper pillow company makes pillows and sells them to motel chains. The plant is trying to minimize cost in the production of pillows. The cost in the production of 2x Squared - 96x + 6837 , where x represents the number of lots of 100 pillows made and C(x) represents the cost of manufacturing the pillows. How many pillows should be produced and sold for the company`s cost to be minimized? what is the minimum cost? 
.
C(x) = 2x^2 - 96x + 6837
where 
x is in lots of 100 pillows
.
Both question can be answered by finding the vertex.
Find it by completing the square to form the "vertex" form of a parabola:
y= a(x-h)^2+k 
where 
(h,k) is the vetex
.
C(x) = 2x^2 - 96x + 6837
C(x) = 2(x^2 - 48x + ___) + 6837
C(x) = 2(x^2 - 48x + 576) + 6837 - 1152
C(x) = 2(x - 24)^2 + 5685
.
Vertex is at (24, 5685)
.
How many pillows should be produced and sold for the company`s cost to be minimized? 
24 lots
or 
2400 pillows
.
what is the minimum cost? 
$5685