Billy goes to Philadelphia (obviously to get a very good Philly cheese steak). To lower his risk of bladder cancer, however, Billy must limit his Philly’s cheese limit to $52g$. Assume that Billy can order his Phillys in three different sizes, as follows:
• Small Philly: costs $\$ 3.25$, comes on a rectangular bread of$8$cm by$24$cm • Medium Philly: costs$\$4.25$, comes on a rectangular bread of $11$ cm by $27$ cm
• Large Philly: costs $\$ 5.25$, comes on a rectangular bread of$14$cm by$30$cm Assume that the density of cheese is$1 \frac{g}{cm^3}$, and that the cheese on each of Billy’s possible Phillys have a$.01\$ cm thickness of cheese that covers each of the two sides of the cut bread. Assuming that Billy has an unlimited amount of money for his Phillys, and that Billy will not leave a single bit of Philly to go to waste, what is the maximum possible amount of Billy’s Phillys, and how much will he have to pay for them?