12.The supply for a particular item is given by the function
. Find the producer's surplus if the equilibrium
producer's surplus if the equilibrium price of a unit
.A retailer anticipates selling
units of its product at a uniform rate over the next year. Each time the retailer places an order for
units, it is charged a flat fee of
. Carrying costs are
per unit per year. How many times should the retailer reorder each year and what should be the lot size to minimize inventory costs? What is the minimum inventory cost?
For a particular commodity, the demand function is
.A hotel rents
rooms at a rate of
per day. For each
increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
13.You are sleeping on an air mattress, which forms a rectangular "box" shape. The length and width don't change, but
't change, but throughout the night the height of the mattress is decreasing. The rate at which it decreases varies over time: at the beginning it is just shrinking a tiny bit, but after a while it starts shrinking faster. If the height of the of the mattress follows the formula h=18-0.2x^2, where h is the height in inches and x is the time in hours, and the length of the mattress is always 74 inches, and the width of the air mattress is always 54 inches, please find the rate at which the VOLUME of the air mattress is changing after 2 hours. V ' =
cubic inches per hour after 2 hours. (Round to one decimal place, but take a picture of your work and send it to me if you're worried your answer might be slightly off.)