Problem Name

Problem Description

Notes

business_calculus_11

Suppose melting snow causes a river to overflow its banks and is the number of inches of water on Main Street hours after the melting begins.
(a) If , by approximately how much will the water level change during the next half-hour?
(b) Which of the following two conditions is the better news?
    (i)
    (ii) ?

business_calculus_12

A rectangular garden of area 75 square feet is to be surrounded on three sides by a brick wall costing $10 per foot and on one side by a fence costing $5 per foot. Find the dimensions of the garden such that the cost of materials is minimized.

business_calculus_13

Find the dimensions of the rectangular garden of greatest area that can be fenced off (all four sides) with 300 meters of fencing.

business_calculus_14

A ship uses dollars of fuel per hour when traveling at a speed of miles per hour. The other expenses of operating the ship amount to $2000 per hour. What speed minimizes the cost of a 500-mile trip?

business_calculus_15

A canvas wind shelter for the beach has a back, two square sides, and a top. Find the dimensions for which the volume will be 250 cubic feet and that requires the least possible amount of canvas.

business_calculus_16

A closed rectangular box is to be constructed with a base that is twice as long as it is wide. Suppose that the total surface area must be 27 square feet. Find the dimensions of the box that will maximize the volume.

business_calculus_17

A bookstore is attempting to determine the economic order quantity for a popular book. The store sells 8000 copies of this book per year. The store figures that it cost $40 to process each new order for books. The carrying cost (due primarily to interest payments) is $2 per book, to be figured on the maximum inventory during an order-reorder period. How many times a year should orders be placed?

business_calculus_18

A travel agency offers a boat tour of several Caribbean islands for 3 days and 2 nights. For a group of 12 people, the cost per person if $800. For each additional person above the 12-person minimum, the cost per person is reduced by $20 for each person in the group. The maximum tour group size is 25. What tour group size produces the greatest revenue for the travel agency?

business_calculus_19

A store manager wants to establish an optimal inventory policy for an item. Sales are expected to be at a steady rate and should total items sold during the year. Each time an order is placed, a cost of dollars is incurred. Carrying costs for the year will be dollars per item, to be figured on the average number of items in storage during the year. Show that the total inventory cost is minimized when each order calls for items.

business_calculus_20

A one-product firm estimates that its daily total cost function (in suitable units) is and its total revenue function is . Find the value of that maximizes the daily profit.