Math 141 WIR5_Dr. Rosanna Pearlstein
1. Write a system of inequalities whose solution set is the inside of the triangle with vertices
,
and
.
Many of these problems are from our textbook, Finite Mathematics, by Tan.
2. Graph each of the following sets of inequalities, and indicate whether the solution set is bounded
or unbounded.
{
{
{
3. Solve the linear programming problems listed below:
Minimize
subject to {
Maximize
subject to {
Minimize
subject to {
4. 3.2 # 10: Agriculture-Crop planning. A farmer plans to plants two crops, A and B. The cost
of cultivating Crop A is $40/acre, whereas the cost of cultivating Crop B is $60/acre. The farmer
has a maximum of $7400 available for land cultivation. Each acre of Crop A requires 20 laborhours, and each acre of Crop B requires 25 labor-hours. The farmer has a maximum of 3300
labor-hours available. If he expects to make a profit of $150/acre on Crop A, and $200/acre on
Crop B, how many acres of each crop should he plant to maximize his profit?
5. 3.3 # 39 Mining. Perth Mining Company operates two mines for the purpose of extracting gold
and silver. The Saddle Minecosts $14,000/day to operate, and it yields 50oz of gold and 3000oz
of silver each day. The Horseshoe Mine costs $16,000/day to operate, and it yields 75oz of gold
and 1000oz of silver each day. Company management has set a target of at least 650oz of gold
and 18,000oz of silver. How many days should each mine be operated so that the target can be
met at a minimum cost? What is the minimum cost?
6. Madison Finance has a total of $20 million earmarked for homeowner loans and auto loans. On
the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12%
annual rate of return. Management also has stipulated that the total amount of homeowner loans
should be greater than or equal to 4 times the amount of automobile loans. Determine the total
amount of loans of each type Madison should extend to each category to maximize its returns.