Question

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 Use the graphical method to solve this model (an approximation is fine, you can type the answer in your R Notebook if you’re not comfortable graphing) (c) Formulate the dual model algebraically (d) Use the graphical method to solve the dual model (an approximation is fine, you can type the answer in your R Notebook if you’re not comfortable graphing) (e) Interpret the dual results

Answer 1

Grain needs oeit vegetable heel . 8 чпі)- 1245 uni nit) 5 vegetable 5。 25 Max Ve iS 55x 245

sam optimum soln is c o poblem 1 25 2. 31S 0.S (0-315,o) o.70