Question 1139948
i solved this graphically as shown below:


<img src = "http://theo.x10hosting.com/2019/042701.jpg" alt="$$$" >


the area of the graph that is not shaded is the region of feasibility.


to find that region, i graphed the opposite of the inequalities formed by the constraints of the problem.


the constraints of the problem were:


3x + 5y <= 45
x >= 0
y >= 0


i graphed:


3x + 5y >= 45
x <= 0
y <= 0


the corner points of the feasible region are where the maximum / minimum solutions lie.


the objective function, which was profit = 160x + 240y, was evaluated at each of these corner points.


at (0,9), the profit was 240 * 9 = 2160


at (15,0), the profit was 160 * 15 = 2400.


maximum profit was 2400 when 15 chains saws and zero chippers were assembled.


unfortunately, there was no happy middle ground for maximum profit.


for example, when x = 5, y = 6 and the profit was 160 * 5 + 240 * 6 = 2240.


that was actually better than one of the corner points but not better than the other.