THE TABLE PRODUCTION PROFIT PROBLEM
Our company makes two tables. Each requiring a different machine with
a build crew of 120 man hrs for construction and a packaging crew
of 65 man hours available.
TABLE1 requires 6 construction hours and 8 packaging hours with a $200 profit.
TABLE2 requires 12 construction hrs. and 4 packaging hours with a $240 profit.
SOLVE FOR MAX PROFIT
Let x1 be the number of TABLE1 to produce.
Let x2 be the number of TABLE2 to produce.
MAXIMIZE PROFIT EQUATION 200x1 + 240x2 = Z (PROFIT)
CONSTRUCTION EQUATION 6x1 + 12x2 <= 120
PACKAGING EQUATION 8x1 + 4x2 <= 64
The solution array/equations
Z - 200x1 - 240x2 + 0 + 0 = 0
0 + 6x1 + 12x2 + s1 + 0 = 120
0 + 8x1 + 4x2 + 0 + s2 = 64
Where s1 and s2 are the slack variables.
ANSWERS: PROFIT $2720 x1=4 x2=8
GIVING 6*4 + 12*8 = 120
AND 8*4 + 4*8 = 64
So to me the problem giver knew the answer and did not want to look too foolish.
Good luck on your next product mix.
The simplex on the web solution,
initial scan and answer.
