Ollie is catering a dinner party for more than 26 guests. Each guest has a choice between a vegetarian dinner or a steak dinner.
The vegetarian dinner is $20 per plate and the steak dinner is $30 per plate. Ollie can spend no more than $690 on the entire party. If Ollie wants to purchase the most amount of food and still stay within budget, which combination of vegetarian and steak dinners is optimal?
Using the graph that is included, look at the points given. For example (30, 3). There would be 30 vegetarian dishes and 3 steak dinners for a total of 33 meals. If that is plugged into the cost equation 20(30)+3(30) it would equal $690. The next point (33, 1) would cost 20(33) + 30(1) = $690 and but gives 34 meals. However, 34 vegetarian meals would only cost 20(34)=$680 and have 34 meals.
If both types of meals need to be purchased, 33 vegetarians and 1 steak. If only vegetarians are purchased, the cost is cheaper by $10.
The vertex will be a maximum because the equation is negative, meaning the parabola opens downwards and will have a maximum point but no minimum point as it will get infinitely smaller.
