Set up the system of linear inequalities and the objective profit function for the given scenario: A pharmaceutical company makes two types of vitamins at its New Jersey plant - a highpotency, anti-oxidant vitamin and a vitamin enriched with added calcium. Each high-potency vitamin contains, among other things, 500 units of vitamin C and 40 units of calcium and generates a profit of $0.10 per tablet. A calcium-enriched vitamin tablet contains 100 units of vitamin C and 400 units of calcium and generates a profit of $0.05 per tablet. Each day the company has available 235,000 units of vitamin C and 156,000 units of calcium for use. Assuming that all vitamins made are sold, how many of each type of vitamin should be manufactured to maximize profit?