Finite Math Test #1 Oct. 9, 2000 A Track R. Hammack Name: ________________________ Score: _________

(1) Multiply the matrices.

 [ 1 3 ] [ 0 1 2 ] = 7 1 -5 2 5

(2) Sketch the solutions of the following system of inequalities.

 2x1 + x2 ≤ 6 x1 + x2 ≤ 4 x1 ≥ 0 x2 ≥ 0

(3)

Maximize

subject to ...

P = x1 + x2

 2x1 + x2 ≤ 6 x1 + x2 ≤ 4 x1 ≥ 0 x2 ≥ 0

You may use any method. (However, notice that you sketched the feasible region in the previous problem. Feel free to use that information to solve this problem.)

(4) Use Gauss-Jordan Elimination to solve the following system of equations:

 2x1 + 2x2 + x3 = 9 2x1 + x2 + 2x3 = 11 x1 + x2 + x3 = 6

(5) Use the simplex method to solve the following problem.

A hippie farmer wants to sell three crops -- apples, beans, and corn -- at the local Farmer's Market. He reckons it will take him 1 hour to harvest each bushel of apples, 2 hours to harvest each bushel of beans, and 1 hour to harvest each bushel of corn. Each bushel of apples weighs 20 pounds, each bushel of beans weighs 10 pounds, and each bushel of corn weighs 5 pounds. Apples sell for \$15 per bushel, beans sell for \$10 per bushel, and corn sells for \$4 per bushel. He has a maximum of 40 hours in which to harvest the crops. Given that his aging pick-up truck can haul at most 1000 pounds of produce, how many bushels of apples, beans, and corn should he take to the Farmer's Market to realize a maximum profit? (Assume he sells everything he brings to the market.)