Math 201 test 4, summer 2014
5-2, 5-3, 6-1, 6-2,7-3
Name___________________
1. For the linear programming problem: Minimize C = 5x + 2y subject to
x  3 y  15
2 x  y  20
x, y  0
a. (8pts) Graph the feasible region by solving the system of linear inequalities
(constraints);
b. (4pts) Find corner points of the feasible region;
c.
(6pts) Find the minimum value of C and indicate where it occurs.
2. (7pts each part) Given the linear programming problem:
2 x1  x 2  8
Maximize P  6 x1  2 x2 subject to x1  2 x 2  10
x1 , x 2  0
a. (2pts) Convert the problem constraints into a system of equations using slack
variables;
b. (2pts) How many basic variables and how many nonbasic variables are associated with the
system in part a? List them.
c. (10pts) Solve the linear programming problem using Simplex Method.
3. (7pts) (manufacturing) A company manufactures outdoor furniture consisting of regular
chairs, rocking chairs, and chaise lounges. Each piece of furniture passes through three
different production departments: fabrication, assembly and finishing. Each regular chair
takes 1 hour to fabricate, 2 hours to assemble, and 3 hours to finish. Each rocking chair takes
2 hours to fabricate, 2 hours to assemble, and 3 hours to finish. Each chaise lounge takes
3 hours to fabricate, 4 hours to assemble, and 2 hours to finish. There are 2,500 laborhours available in the fabrication department, 3000 in the assembly department, and
3,500 in the finishing department. The company makes a profit $17 on each regular chair,
$24 on each rocking chair, and $31 on each chaise lounge. How many chairs of each type
should the company produce in order to maximize profit? What is the maximum profit?
a. (4pts)Assign variables to unknowns and write the objective function;
b. (6pts) Set up the constraints;
c. (bonus: 5 pts) Use simplex method to find the maximum profit. (use back of page)
4. How many 4 letter code words are possible using the first 8 letters of the alphabet if
a. No letter can be repeated?
b. Letters can be repeated?
c. Adjacent letters cannot be alike?