Question 1194261
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Let x = acres of tomatoes
Let y = acres of strawberries<br>
The constraints are....<br>
x>=0; x<=37  max 37 acres of tomatoes
y>=0; y<=23  max 23 acres of strawberries<br>
3x+10y<=300  max 300 hours of labor
20x+8y<=800  max 800 tons of fertilizer<br>
Use Desmos.com to draw the graph.  Graph the OPPOSITE of each inequality (e.g., 3x+10y>300); that way the UNSHADED region will be the feasibility region.<br>
The numbers in the problem require slightly ugly arithmetic to find the corners of the feasibility region; so I won't go any farther with specifics about solving the problem.<br>
Note, however, that it is NOT necessary to find the coordinates of all corners of the feasibility region and evaluate the objective function at each one.<br>
It is easy to determine which corner of the feasibility region will produce that maximum value of the objective function (profit), by comparing the slope of the objective function to the slopes of the constraint boundary lines.<br>
The slopes of the two constraint boundary lines are -3/10 and -5/2.<br>
For the first case where the profits are $40,000 per acre for strawberries and $30,000 per acre for tomatoes, the slope of the objective function is -3/4.  Because -3/4 is between -3/10 and -5/2, the maximum profit will be where the two slanted constraint lines intersect.<br>
You can do the ugly arithmetic to find the actual numbers of acres of strawberries and tomatoes.<br>
Note your description for the second case is incorrect....<br>
But the slopes of the constraint boundary lines are so much different that making small changes in the profits per acre for either strawberries or tomatoes would not change the result that the maximum profit is where the two constraint boundary lines intersect.<br>