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Optimization Problems Worksheet - Math 105, Sections 10.3 & 10.4 Calculus For Economics & Business Page 4

More Problems

Problem 7. It is estimated that the cost of constructing an oﬃce building that is n ﬂoors high is c(n) =

+ 500n + 600 thousand dollars. How many ﬂoors should the building have in order to minimize the average

cost per ﬂoor? (Answer: 17 ﬂoors)

Problem 8. Find the quantity q of items which maximizes the proﬁt if it is not possible to produce more than

800 items, and if the total revenue and the total cost (in dollars) are given below: (Answer: 650)

R(q) = 5q

0.003q

and C(q) = 300 + 1.1q

Problem 9. An apartment complex has 400 apartments. At $ 400 per month for each apartment all the

apartment will be occupied. Each $20 increase will produce 10 vacancies. Let x denote the number of $ 20

increase. What is the largest revenue that the apartment complex can generate? (Answer: x = 10)

Problem 10. Suppose you run a small independent furniture business. You sign a deal with a customer to

deliver up to 400 chairs, the exact number to be determined by the customer later. The price will be $80 per

chair up to 300 chairs, and above 300, for every additional chair over 300 ordered, the price will be reduced by

$0.20 per chair on the whole order. What are the largest revenue your company can make if the customer

choose to order more than 300 chairs?

Problem 11. There are 320 yards of fencing available to enclose a rectangular ﬁeld. How should this fencing

be used so that the enclosed area is as large as possible? (80

80)

Problem 12. A city recreation department plans to build a rectangular playground having an area of 3600

square meters and surround it by a fence. How can this be done using the least amount of fencing? (Answer:

60 meters)

Problem 13. You are asked to design a cylindrical aluminum can holding a volume of 300cm . If both the

top and the bottom of the can are twice as thick as the sides of the can, what dimensions of the can will

minimize the amount needed. (A cylinder with radius r and height h has a volume given by V = πr h, its

surface area (lids not included) is S = 2πrh.)

Optimization Problems Worksheet - Math 105, Sections 10.3 & 10.4 Calculus For Economics & Business Page 4