submit a complete (parametric) analysis for the CA strawberries and tomatoes farmer's problem:

Whether CA farmer should rent 30 acres from the farm to the north of his property at a cost $200 per acre per season or whether he should rent out land to the owner of the adjoining farm on the south side for $290 per acre per season (in class we examined cost/benefit of going up to allowable increase and decrease). For this assignment you need to examine what happens beyond the limits of the allowable range, i.e. you need to resolve the problem possibly more than once....). For the purpose of this 'assignment', your recommendation should include 'using the land for farming', not just the financial transaction of renting from north at $200 and renting it out to south for $290 (!)

In other words, you can Either rent from north OR rent to south (not both..)

Max 400 S + 300 T

S + T

10S + 3T

8S + 20T

S

T

S , T >0 Non-Negativity

California Grower Question 4: The farmer has 2 alternatives to consider: a) Farmer can rent 30 acres from the farm to the north of property at a cost $200 per acre per season. Net gain: 257.14-200=$57.14 Can add 2.27 acres so gain is: $57.14 x 2.27 = $129.7 b) The owner of the adjoining farm on the south side has offered the grower $290 per acre per season. Net gain: 290-257.14=$32.86 Should farmer 'rent Can 'give' 10.66 acres so gain is: $32.86 x 10.66 = $350.50 out more than 10.66 to owner on Variable Cells the south ??? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$14 Acres Strawberries 21.42857143 0 400 600 100 Optimal solution $D$14 Acres Tomatoes 28.57142857 0 300 100 180 5* - 21.42 acres T* = 28.57 acres Constraints Z* = $17,142.86 Final Shadow Constraint Allowable Allowable Cell Value Price R.H. Side Increase Decrease $E$7 land Resource Used 50 257.1428571 50 2.272727273 10.66666667 $E$8 labor Resource Used 300 14.28571429 300 32 33.33333333 $E$9 Fertilizer Resource Used 742.8571429 0 8001E+30 57.14285714 $E$10 shipping strawberries Resource Used 21.42857143 0 26 1 E+30 4.571428571 $E$11 Shipping Tomatoes Resource Used 28.57142857 0 3 71E+30 8.428571429 Name California Grower Question 4: The farmer has 2 alternatives to consider: a) Farmer can rent 30 acres from the farm to the north of property at a cost $200 per acre per season. Net gain: 257.14-200=$57.14 Can add 2.27 acres so gain is: $57.14 x 2.27 = $129.7 b) The owner of the adjoining farm on the south side has offered the grower $290 per acre per season. Net gain: 290-257.14=$32.86 Should farmer 'rent Can 'give' 10.66 acres so gain is: $32.86 x 10.66 = $350.50 out more than 10.66 to owner on Variable Cells the south ??? Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $C$14 Acres Strawberries 21.42857143 0 400 600 100 Optimal solution $D$14 Acres Tomatoes 28.57142857 0 300 100 180 5* - 21.42 acres T* = 28.57 acres Constraints Z* = $17,142.86 Final Shadow Constraint Allowable Allowable Cell Value Price R.H. Side Increase Decrease $E$7 land Resource Used 50 257.1428571 50 2.272727273 10.66666667 $E$8 labor Resource Used 300 14.28571429 300 32 33.33333333 $E$9 Fertilizer Resource Used 742.8571429 0 8001E+30 57.14285714 $E$10 shipping strawberries Resource Used 21.42857143 0 26 1 E+30 4.571428571 $E$11 Shipping Tomatoes Resource Used 28.57142857 0 3 71E+30 8.428571429 Name