# Math

posted by .

Could someone work this question out so I understand it. Thanks

The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is a weekly demand of 8 units at the price of \$60.83 per unit [p(8)=60.83].

A)find the price demand equation. Give an exact answer in simplified form. Round all decimal values to the nearest hundreth.

B)At a demand of 25 units per week, what is the price? Round to the nearest cent.

• Math -

dp/dx = k p
dp/p = k dx
ln p = kx + C
p = e^(kx+C) = c e^kx
p(0)= + 100
so
100 = c e^0 = c
so
p = 100 e^kx
p(8) = 60.83
60.83 = 100 e^(k*8)
ln(.6083) = 8 k
k = -.06214
so
p = 100 e^(-.06214 x)

if x = 25
p = 100 e^-(.0214*25)
p = 100 * .5857
p = \$58.57

## Similar Questions

The research department for a hardware chain has determined that at one store the marginal price of x boxes per week of a particular type of nail is: p'(x)=-4000/(2x+15)^3 Find the demand equation if the weekly demand for this type …
2. ### Microeconomics:

Just needing to know if I have done the work correctly with this problem: For the total revenue and marginal revenue the answers are: Price \$20 Quantity 0 TR 0 MR 0 Price \$18 Quantity 1 TR 18 MR 18 Price \$16 Quantity 2 TR 32 MR 14 …
3. ### college/microeconomics

Just needing to know if I have done the work correctly with this problem: For the total revenue and marginal revenue the answers are: Price \$20 Quantity 0 TR 0 MR 0 Price \$18 Quantity 1 TR 18 MR 18 Price \$16 Quantity 2 TR 32 MR 14 …
4. ### Math

Could someone work this question out so I understand it. Thanks The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is a …
5. ### Math

Could someone answer this question so I understand it. Thanks The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is a weekly …
6. ### Math

Could someone work this question out so I understand it. Thanks The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is a …
7. ### calc

I have everything right but the last question asking how many cases per week The consumer demand equation for tissues is given by q = (97 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) …
8. ### brief calculus

I have everything right but the last question asking how many cases per week The consumer demand equation for tissues is given by q = (97 − p)^2, where p is the price per case of tissues and q is the demand in weekly sales. (a) …
9. ### marketing

You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for its hamburgers in order to maximize its weekly revenue. To make life as simple as possible, you assume …
10. ### Calculus

The consumer demand equation for tissues is given by q = (97 − p)2, where p is the price per case of tissues and q is the demand in weekly sales. (a) Determine the price elasticity of demand E when the price is set at \$26. (Round …

More Similar Questions