Exam Review Suggestions	
•	For a given linear programming problem, determine the feasible space and its corners and 
determine the optimum solution.  	  	
•	Be able to set up a linear programming story problem.  (It may have more than 2 variables.)

Sample Problems

1. A flower shop makes two different kinds of flower arrangements.  The first kind uses 6 roses, 3 carnations and 4 sprigs of baby’s breath.  The other kind uses 3 roses, 8 carnations and 2 sprigs of baby’s breath.  The shop has available 50 roses, 60 carnations and 35 sprigs of baby’s breath.  The profit earned on the first kind of flower arrangement is $4 per arrangement, and the profit earned on the second kind is $6 per arrangement.  The shop owners would like to know how many of each type of arrangement should be made to maximize profit.

a. Write the constraints and profit formula for this problem. Do not solve it.

b. For each of the production policies below, say whether or not this policy is feasible. If not, say why not; if it is feasible, what would the profit be for that policy?
	i. Make 5 of each kind of arrangement.

ii. Make 5 of the first kind of arrangement and 7 of the second.

2. Use linear programming to find all pairs (x, y) which maximize P = 5x + 3y subject to the constraints shown below. Also find the maximum value for P.
2x + 3y < 26
4x + 4y < 40
 x > 1, y > 2

3. A paper recycling company uses scrap cloth and scrap paper to make two different grades of recycled paper.  A single batch of grade A recycled paper is made from 25 lb of scrap cloth and 10 lb of scrap paper, whereas one batch of grade B recycled paper is made from 10 lb of scrap cloth and 20 lb of scrap paper.  The company has 100 lb of scrap cloth and 120 lb of scrap paper on hand.  A batch of grade A paper brings a profit of $500, and a batch of grade B paper brings a profit of $250.  What amounts of each grade should be made?   Just find the profit function and a system of inequalities representing the constraints. You do not have to find the feasible region, corner points, etc.

4. Use a graphical procedure to solve the following linear programming problem.  (Be sure to show appropriate work as demonstrated in class.)
Find the maximum value of P, where P = 10x + 100y subject to the constraints: