Many vitamin C products are made from ascorbic acid, which is derived from corn. A small dietary supplement company makes two types of vitamin C supplements: capsules and chewable tablets. To produce 1 kilogram of vitamin C capsules, 30 kilograms of corn, 2.3 hours of manufacturing time, and 2 hours of packaging time are required. To produce 1 kilogram of vitamin C tablets, 40 kilograms of corn, 4.2 hours of manufacturing time, and 1 hour of packaging time are required. Each week, the company has 2,000 kilograms of corn from its suppliers and allocates 180 hours of equipment time for manufacturing and 110 hours of packaging equipment time for vitamin C supplements. One kilogram of vitamin C capsules generates a profit of $9.50, and one kilogram of chewable tablets generates a profit of $12. 

a. Formulate and solve an LP model to maximize the profit contribution from the two vitamin C products. How many kilograms of vitamin C capsules and tablets should the company produce each week? What is the maximum profit the company can make? 

b. If the per-kilogram profits of vitamin C capsules and tablets increase to $11.50 and $16, respectively, how much of each product should the company make? What is the corresponding profit amount?