# MAT131 Bonus Lab

## Optimization Problems

### Objectives

- Practice solving optimization problems using Excel.

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?