Question 1 - Linear Programming a. A farmer plans to grow three cropscarrot, pakchoy, and tomatoin the forth-coming season in hi farm, which spans 60 hectares. Each crop requires nitrogen, phosphoros, potassium, and micronutrients The resource requirement for each crop and the total resources available are as follows: Nitrogen Phosphorus Potassium Micronutrients (kg/ha) (kg/ha) (kg/ha) (kg/ha) Crops Revenue Yield (Rp/kg) Productivity (ton/ha) Carrot 10000 300 Pakchoy 12500 Tomato 11500 240 Total available nutrients (kg) 475 225 700 300 110 209 99 300 110 500 250 600 152 2000 9100 24000 7500 Nowadays, the fertilizers that contain NPK (nitrogen, phosphorus, potassium) and micronutrients ca be bought separately. Given the resource and land constraints, the farmer wants to know how many hectares of each type of crop to plant in the season to maximize revenue. Formulate a linea programming model for the above problem. b. The following table is the MS Excel Solver solution of a linear programming model Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$14 X1 16 0 15 5.00 3.5 $B$15 X2 6 0 20 2 4 $B$16 X3 6 0 30 2 4 30 14 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $F$10 X1 Constraint 30 5000 50 20 27 $F$11 X2 Constraint 10000 30 20 $F$6 X3 Constraint 280 2000 350 70 100 $F$7 Z Constraint 140 0 150 1E+30 1E+30 i. Explain the shadow price of the three constraints. ii. What are the ranges of the objective function coefficients X1, X2, and X3 that wil not change the optimal solution