Linear programming statistics question

O'Brien family owns 410 acres of farmland on which they grow corn and tobacco. Each acre of corn costs $105 to plant, cultivate and harvest; each acre of tobacco costs $210. O'Briens have a budget of $52,500 for the next year. The government limits the number of acres of tobacco that can be planted to 200. The profit from each acre of corn is $325; the profit from each acre of tobacco is $500. O'Brien family wants to know how many acres of each crop to plant in order to maximize the profit. (a) Formulate a linear programming model for this problem: Maximize P 2 325m + 5003; a: + y S 105 4102*: + 20011; S 52, 500 y g 210 @920 Maximize P = 3253: + 5009 a: -l- y S 410 105:1: + 2101/ S 52, 500 y g 200 32,3120 (0) Identify the optimal solution. How much is the maximum profit? a: = 410, y = 0 is the optimal solution, and the maximum profit is $133,250 a: = 320, y = 90 is the optimal solution, and the maximum profit is $149,000 m = 500,19 2 0 is the optimal solution, and the maximum profit is $162,500 a: = 0, y = 200 is the optimal solution, and the maximum profit is $100,000 a: = 210, y = 200 is the optimal solution, and the maximum profit is $168,250 a: = 100, y = 200 is the optimal solution, and the maximum profit is $132,500