Finite Math Exam 1 Review - Faculty Web Pages

FM Lial 9 th ed
FM Exam 1 Review F09 O’Brien
6b. x = # of batches of cars. y = # of batches of jets
Minimize cost, C = 120x + 100y, subject to the following constraints:
6x + 3y ≤ 150 2.5x + 7.5y ≤ 150 5x + 5y ≤ 150 x ≥ 0 y ≥ 0
6x + 3y + s 1 = 150
2.5x + 7.5y + s 2 = 150
5x + 5y + s 3 = 150
–120x – 100y + C = 0
⎡ 6 3 1 0 0 0 150⎤
⎢
⎥
⎢
2.
5 7.
5 0 1 0 0 150
⎥
⎢ 5 5 0 0 1 0 150⎥
⎢
⎥
⎣−120
−100
0 0 0 1 0 ⎦
7a. Maximum f is 264 when x = 16, y = 4, z = 0, s 1 = 0, s 2 = 16, and s 3 = 0
7b. Maximum f is 18 when x = 5, y = 4, z = 0, s 1 = 0, s 2 = 0, and s 3 = 15
7c. x = # model A hibachis. y = # model B hibachis
Maximize profit, P = 2x + 1.5y, subject to 3x + 4y ≤ 1000 6x + 3y ≤ 1200 x ≥ 0 y ≥ 0
They should produce 120 model A hibachis and 160 model B hibachis to earn a maximum
profit of $480. There will be no raw material left over.
8a. Maximum P = 12 when x = 0, y = 6, s 1 = 0, s 2 = 15
8b. Minimum C =
Part Two
66 3 20 12 when x = , y = , s1 = , s2 = 0, and s 3 = 0
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7 7 7
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