Math 103. Homework 9. Due 4/20/02

1. [80, p. 317] As a result of increasing energy costs, the growth rate of the profit of the 4 year old Venice Glass-blowing Company has begun to decline. Venice's management, after consulting with energy experts, decides to implement certain energy conservation measures aimed at cutting energy bills. The general manager reports that, according to his calculations, the growth rate of Venice's profit should be on the increase again within 4 years. If Venice's profit (in hundreds of dollars) x years from now is given by the function


P(x) = x3-9x2+40 x+50        (0 £ x £ 8)
determine whether the general managers forecast will be accurate.

2. The weekly demand for video discs manufactured by the Herald Record Co. is given by


p=-0.0005 x2 +60
where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with producing theses discs is given by


C(x)=-0.001x2 +18 x +4000
where C(x) denotes the total cost incurred in pressing x discs. Find the production level that will yield a maximum profit for the manufacturer. What is this maximum profit?

3. [51, p. 352] The quantity demanded per month of the Sicard wristwatch is related to the unit price by the equation


p= 50
0.01 x2 +1
        (0 £ x £ 20)
where p is measured in dollars and x in units of a thousand. How many watches must be sold to yield a maximum revenue?

4. [15, p. 366] If exactly 200 people sign up for a charter flight, the LWP Travel Agency charges $ 300 per person. However, if more than 200 people sign up for the flight (assume this to be the case) then each fare is reduced by $ 1 for each additional person. Determine how many passengers will result in a maximum revenue for the travel agency. What is the maximum revenue? What would be the fare per passenger in this case?

5. You wish to construct a closed rectangular box that has a volume of 4ft3. The length of the base of the box will be twice as long as its width. The material for the top and bottom of the box costs 30 cents/square foot. The material for the sides of the box costs 20 cents/square foot. Find the dimensions of the least expensive box that can be constructed.

Suggested Exercises Section 4.3.- 1-10, 12-20. Section 4.4.- 19, 20, 44, 49, 55. Section 4.5.- 3, 8, 10, 14, 21, 22. Section 5.1.- 1-24.