Homework 3.6

question 6

Suppose that for a company manufacturing calculators, the cost, revenue, and prot equations are given by Next quest C=90,000+20x, R=3DO -5, P=RC where the production output in 1 week is x calculators. If production is increasing at a rate of 600 calculators per week when production output is 4,000 calculators. Find the rate of increase (decrease) in cost, revenue, and prot. A) Costs are l at the rate of $ per week at this production level. (Simplify your answer.) A 13-toot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away from the wall at a constant rate of 3 feet per second. How test is the top of the ladder sliding down the wall when the bottom is 5 feet from the wall? The ladder is sliding down the wall at a rate of Wsec. (Type an integer or a simplied fraction.) A retail store estimates that weekly sales 5 and weekly advertising eosm x (both in dollars) are related by s = 60,000 - 40,000 e '0'0004". The current weekly advertising costs are $2,500, and these costs are increasing at a rate of $300 per week. Find the current rate of change of sales. The current rate of change of sales is 5 per week. (Round to the nearest dollar as needed.) dV An oil tanker aground on a reel is forming a circular oil slick about 0.2 foot thick. To estimate the rate 3 (in cubic feet per minute) at which the oil is leaking from the tanker, it was found that the radius of the dR dV slick was increasing at 0.42 loot per minute (F = 0.42) when the radius R was 600 feet. Find 3' using E z 3.14. dV _ 7 dt ' (Type an integer or a decimal. Round to the nearest whole number as needed.) ft3 (min