MAT131 Bonus Lab

Optimization Problems


This is an optional lab but if you complete each problem correctly, I'll give you 10 bonus points.

Problem 1

A farmer has 100 acres of land and wants to plant a mixture of potatoes, corn, and cabbage. It costs her $400 to produce an acre of potatoes, $160 to produce an acre of corn, and $280 to produce an acre of cabbage but she only has $20,000 available to spend. She can earn $120 per acre of potatoes, $40 per acre of corn, and $60 per acre of cabbage. How many acres of each crop should she plant in order to maximize her earnings? What are her maximum earnings?

Problem 2

The manager of a state park wants to replace the picnic tables in the park. Each redwood table requires 8 hours to make, requires no stain, and costs (for material and supplies) $160. A table made of Douglas fir takes 7 hours to build, 2 hours to stain, and costs $140. Each white spruce table takes 8 hours to make, 2 hours to stain, and costs $130. The park manager has only $14,960 available to spend for supplies and materials. To save money he is using volunteer labor and has 898 man-hours available for building the tables and 228 man-hours available for staining the tables. How many of each type of table should he make in order to maximize the total number of tables?

Problem 3

Suppose a gerbil breeder needs at least 60 units per day of nutrient A and at least 30 units per day of nutrient B. Mighty Good gerbil food supplies 1 unit of nutrient A and 2 units of nutrient B per packet at a cost of 30 cents a packet. Sleek Coat gerbil food supplies 3 units of nutrient A and 1 unit of nutrient B per packet at a cost of 20 cents a packet. How many packets of each kind of gerbil food should the breeder use each day to minimize the cost? What is the minimum cost?