Algebra word problem

Question

Cherries cost $4/lb. Grapes cost $2.50/lb. You can spend no more than $15 on fruit, and you need at least 5 lb in all. Create a graph showing the amount of each fruit you can buy.

Answer 1

This would not be a simple graph. What you can graph are optimum and minimum plots but even then there are 2 possibilities depending on how you define 'optimum' and 'minimum' - do you find the max/min amount of fruit for $15 or do you find the max/min amount of money spent for 5 pounds or more?

If you want to maximize pounds of fruit, then you spend all $15 on 6 pounds of grapes because any decrease in the amount of grapes does not allow an equal increase in the amount of cherries. Obviously, to minimize pounds of fruit, you cannot go below 5 pounds because of the limits, so you could buy just 5 pounds of grapes for $12.50. You could also buy less grapes and replace with the equal value of cherries or more back up to the $15 limit.

The entire graph (if I picture it in my mind accurately) would be 2 curved segments and all the area between them.