# Linear Programming Word Problem - Need Min/Max and Constraints

Mr. Randolph wants to take his little brother Everett and 10 of his little friends to Pistol Petes Pizza. A large pizza (including tokens for games) costs 20 and a pitcher of soda costs $5. Being a teacher, Mr. Randolph is very concerned about how much money he is going to spend, so he does not want to spend more than$100. Also, he is only willing to buy at most 11 pitchers of soda, but knows that he needs to have enough pizza and soda for all of the kids.

Model this scenario graphically, and then determine the best possible solutions.

Having difficulty determining the min/max and constraints.

I've posed that C=20x+5y. Normal constraints of x>=0, y>=0, and 20x+5y<=100. When I try to graph this, I don't get useable test points.

• This problem statement is incomplete: what is it that you want to maximize or minimize? Also, you should define what your variables represent: what is $x$? what is $y$? By explicitly writing down what they represent, you can avoid issues later. – Matthew Conroy Oct 7 '17 at 0:22
• You should specifically say that "x is the number of pizzas ordered and y is the number of sodas". You also have the constraint that y<= 11. In order to decide what "needs to have enough pizza and soda for all of the kids" means you will need to know how much pizza and soda each kid can consume. Finally, to "determine the best possible solutions" you will need to know what "best" means here. Is it the least amount of money? The most pizzas? The most soft drink? – user247327 Oct 7 '17 at 0:26
• I want to minimize the cost. The total cost cannot exceed 100 dollars. There are 11 children total ("Everett and 10 of his friends"), but no rationale for the amount they can consume or drink. Based on the vagueness, I've set to reach the solution of how much pizza and soda can we get for 100 dollars that would "reasonably" feed 11 kids total. – Jake Ryan Oct 7 '17 at 0:32
• You are going to have to introduce some information about how much pizza and soda each kid needs. But this is really not a linear programming problem: you just find the cost to feed/water a kid, multiply it by 11, and that's your minimum cost. – Matthew Conroy Oct 7 '17 at 0:42
• Yes, you do not have enough information. If each person requires $x$ pizzas and $y$ pitchers of soda, then each person costs $20x+5y$ and so the total cost is $11*(20x+5y)$. Fill in $x$ and $y$ with the actual requirements, and you are done. There is no linear program here. – Matthew Conroy Oct 7 '17 at 3:27