SOLUTION: 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

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?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
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
RELATED QUESTIONS
The cost of 6 bedspreads and 8 pillows is $448.12. Three bedspreads and 10 pillows cost... (answered by ewatrrr)

You buy a pattern and enough material to make 2 pillows. The pattern costs $5. Each... (answered by checkley77,rfer)

3. A company is trying to minimize their costs. Their accountant comes up with the... (answered by josgarithmetic,ikleyn)

Sarah wants to buy new pillows for her room.Which store offers the best buy on pillows? (answered by ikleyn,josgarithmetic)

A manufacturing company receives orders for engines from two assembly plants. Plant I... (answered by Theo)

A rectangular pillow has a length of 14 in., width of 12 in., and height of 3 in.... (answered by FrankM)

The cost of 4 pillows, plus 5% sales tax, was 46.20. How much did each pillow cost? (answered by jim_thompson5910,RAY100)

I just need to know how I would set up this equation. the Question is A company makes tv... (answered by rfer)

Allie needs 65 centimeters of fabric for the pillow she is making. The fabric costs $4.20 (answered by josmiceli)