Question

Suppose the demand for a certain brand of a product is given by ​D(p)equals=StartFraction negative p squared Over 116 EndFraction−p2116plus+200200​, where p is the price in dollars. If the​ price, in terms of the cost​ c, is expressed as p (c )equals 2 c minus 10p(c)=2c−10​, find the demand function in terms of the cost.

Answer 1

The demand function in terms of the cost c is found by substituting p(c) = 2c - 10 into the original demand function, yielding D(c) = -c^2/29 + 10c/29 + 75/29.

Step-by-step explanation:

The original demand function D(p) is given by D(p) = -p2 / 116 + 200, where p is the price in dollars. The price in terms of cost c is given by p(c) = 2c - 10. To find the demand function in terms of cost, substitute the expression for p in terms of c into the demand equation.

Performing the substitution, we get:

D(c) = - (2c - 10)2 / 116 + 200

Simplifying the equation:

D(c) = - (4c2 - 40c + 100) / 116 + 200

= -4c2/116 + 40c/116 - 100/116 + 200

= -c2/29 + 10c/29 + 75/29

The simplified demand function D(c) shows the demand in terms of the cost c.

Answer 2

The demand function in terms of cost is
`D(c) = [([40c- 100 -4c^2 \ ]))/(116) ] + 200`

Step-by-step explanation:

From the question we are told that

The demand for a certain brand of a product is

`D(p) = (-p^2)/(116) + 200 ----(1)`

The​ price, in terms of the cost​ c, is expressed as

`p(c) = 2c -6 -----(2)`

Now substituting equation 2 into equation 1

So

`D(c) = - [((2c -10 )^2))/(116) ] + 200`

`D(c) = - [([4c^2 + 100 -40c \ ]))/(116) ] + 200`

`D(c) = [([40c- 100 -4c^2 \ ]))/(116) ] + 200`