The demand function for a certain brand of mattress is given

The demand function for a certain brand of mattress is given by p = 600e^-0.04x where p is the unit price in dollars and x (in units of a hundred) is the quantity demanded per month. (Round your answers to the nearest integer.) (a) Find the number of mattresses demanded per month if the unit price is set at $400/mattress. mattresses (b) Use the results of part (a) to find the consumers\' surplus if the selling price is set at $400 per mattress.$ Estimate the present value of an annuity if payments are $1300 monthly for 15 years and the account earns interest at the rate of 10%/yr compounded continuously.

Solution

a) P = 600e^-0.04x

p = $ 400/mattress

400 = 600e^-0.04x

solve for x: ln(4/6) = -0.04x

x = 10.136 = 10 mattress

b) revenue = 400*10 = $ 4000

Deman = p*no. of matress = 400*10 = $4000

There is no surplus 0 $