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y = rods
at most 100 units of steel a day
at least 20 girders
at least 60 rods
girder is $8
rod is $6
maximize the profits
p(x,y) = 8x+6y max profit is (40,60) 40 girders and 60 rods will produce for a maximum profit of $680.
at least 20 girders = x≥20
at least 60 rods = y≥60
at most 100 units of steel a day = x+y≤100
(20,60)
(20,80)
(40,60)
Seven steps to solve a linear programming problem:
1. Define variables.
2. Write the objective function (GOAL).
3. Write the system of inequalities based on the constraints of the problem.
4. Graph the system of inequalities and the feasible region (*Hint decide scale first based on intercepts).
5. Identify the vertices (corners) of the feasible region.
6. Evaluate the objective function for the coordinates of the vertices of the feasible region.
7. Identify the coordinates that answer the problem, and ANSWER THE PROBLEM.
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