A farmer is producing Grains and Vegetables with a given set of input mix and water. The input mix includes fertilizer and labor in fixed ratios so they can be treated as one variable, with grains needing 5 units of input and and vegetables needing 50 units of input per acre. Water is also used, grains need 4 units of water and vegetables need 8 units of water per acre. The farmer only has 1,245 units of the input mix and 300 units of water. The profit per acre is $5 for grains and $25 for vegetables. The farmer wants to maximize profits and there is no acreage constraint. (a) Formulate a linear programming model algebraically