Question 1207825
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Tutor @ikleyn provides a lengthy response stating that the problem as posed has no solution, without saying what the problem is.<br>
Tutor @Edwin tells what the problem is with the problem as posted in his first sentence.  A bit more helpful to the student....<br>
His response shows a typical solution using the method found in virtually all references: determine the corners of the feasibility region based on the given constraints and evaluate the objective function at each corner to find the minimum and maximum values of the objective function.<br>
In fact, it is not necessary to evaluate the objective function at each corner of the feasibility region.<br>
You can determine the corners of the feasibility region where the minimum and maximum values of the objective function occur by comparing the slope of the objective function with the slopes of the constraint boundary lines.<br>
The objective function is z=x+5y; in slope-intercept form it is y=(-1/5)x plus some constant, so the slope of the objective function is -1/5.<br>
The maximum and minimum values of the objective function will occur where lines with slopes of -1/5 just touch the feasibility region.<br>
The slopes of the two constraint boundary lines are -2 and -3/2.<br>
Using the diagram Edwin shows in his post, it is clear that lines with slopes of -1/5 will just touch the feasibility region at (0,6) and (0,0), so those are the corners of the feasibility region where the maximum and minimum values of the objective function will occur.<br>
ANSWER: the objective function has maximum value of 30 at (0,6)<br>