James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have bud
geted $3500 for the reception. If the reception hall charges a $50 cleanup fee plus $34 per person find the greatest number of people that they may invite and still have within their budget.
$34 times the number of people plus the $50 cleaning fee has to be less than or equal to $3500
Or
34p + 50 <= 3500
34p <= 3450
p <= 101.470588....
We can have a part of a person attending the reception so we have to drop the remainder/decimal. Therefore the most amount of people that can attend the party and stay within budget is 101.
First thing to do with this problem is to plot the given data in MS excel. We can see in the graph that the minima (lowest point of the graph) is at (4,-2) and the maxima is at (2,3). The critical points are points which the direction changes from one side to another.
