What are the restrictions for graphing Ramesh's exercise plan?

[might hire]

Okay, here is the problem, ; Remesh likes to run outdoors and ride his bicycle at the veledrome. He burns about 400 calories/h running, and 300/h riding his bike. It costs $6/h to ride in the veledrome. Ramesh hopes to develope a weekly exersise program that will burn 4800 calories, cost no more than $24, and require a maximum of 8 hours... Now I need the restrictions to graph this problem, (x=running/h; y=bike/h) I so far have; x (> or equal to) 0, y (> or equal to) 0, x+y (< or equal to) 8, and y (< or equal to) 4. I think I'm missing one, and think it might have to do with the calories, so is 400x+300y (> or equal to) 4800. But would it be applicable to the hour restriction? Thanks in Advance!

 

[verty]

Intuitively, the most calories will be burnt by running. 8 hours of running will burn 3200 calories, so it is impossible to get 4800 from 8 hours of exercise.

When you plot the inequalities, the solution lies in the intersection of the areas. When you plot the fifth inequality (400x + 300y >= 4800) you'll find the areas do not intersect, so there is no solution.