By using the solution and sensitivity analysis obtained with Solver, answer the questions below that correspond...

  

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By using the solution and sensitivity analysis obtained with Solver, answer the questions below that correspond to the following linear programming problem. The corresponding report obtained with Solver is in the last page. X₁ = Number of apple trees to be planted, X-Number of avocado trees to be planted (Total profit) subject to Max Z-5000X₁ + 7000X2 10X₁ +20X₂≤ 1000 2X₁ + 3X₂ <200 X₁ + 2X: ≤2400 25X₁ + 50X35000 10X₁ + 15X15000 X₁, X₂20 (Available fertilizer, in tons) (Available land, in hectares) (Available labor hours) (Available water, in liters) (Available budget, in dollars) 1. How many trees of each type must be planted? 2. What is the corresponding optimal profit? 3. Are there any resources left? Which ones and how much of each? 4. Somebody wants to buy fertilizer at $600 per ton. Is it convenient for the company to sell fertilizer? Up to how many tons should the company sell? Justify your answer 5. If the profit obtained from each apple tree increases from $5000 to $15000 and there is no change in the profit for each avocado tree, how many apple trees and how many avocado trees should be planted? What is the corresponding optimal profit? 6. If the profit obtained from each avocado tree increases from $7000 to $15000 and there is no change in the profit for each apple tree, do the optimal values of the decision variables change? Justify your answer 7. If the available fertilizer increases from 1000 tons to 1001 tons, then the optimal profit increases in $500. Mark the right answer. True ( ) False () 8. If the total number of hectares decreases to 199, the optimal profit does not change because the shadow price or dual value is 0. Mark the right answer. True ( ) False ( ) 9. If I avocado tree is planted, What is the corresponding profit? 10. Some employees wish to work overtime. What is the maximum amount, additional to the regular rate, the company would be willing to pay for each overtime hour? Justify your answer. This is the solution and sensitivity report for Problem 6. They were obtained with Solver. 6769LOSSENH 10 11 456 9 10 A A X1 100 15 16 17 18 19 5000 22159 10 6 Variable Cells 7 8 10 $A$2 X1 $B$2 X2 11 12 Constraints 13 14 C B X2 0 7000 20 3 2 50 15 Cell Name Value Cell Name $C$7 Max Z $C$8 Max Z- $C$9 Max Z- $C$10 Max 2 = $C$11 Max Z- D 100 с 0 Max Z= 1000 200 2500 1000 100 2500 1000 E SENSITIVITY REPORT D 0 500000 -500 ***** Final Reduced Objective Allowable By using the solution and sensitivity analysis obtained with Solver, answer the questions below that correspond to the following linear programming problem. The corresponding report obtained with Solver is in the last page. X₁ = Number of apple trees to be planted, X-Number of avocado trees to be planted (Total profit) subject to Max Z-5000X₁ + 7000X2 10X₁ +20X₂≤ 1000 2X₁ + 3X₂ <200 X₁ + 2X: ≤2400 25X₁ + 50X35000 10X₁ + 15X15000 X₁, X₂20 (Available fertilizer, in tons) (Available land, in hectares) (Available labor hours) (Available water, in liters) (Available budget, in dollars) 1. How many trees of each type must be planted? 2. What is the corresponding optimal profit? 3. Are there any resources left? Which ones and how much of each? 4. Somebody wants to buy fertilizer at $600 per ton. Is it convenient for the company to sell fertilizer? Up to how many tons should the company sell? Justify your answer 5. If the profit obtained from each apple tree increases from $5000 to $15000 and there is no change in the profit for each avocado tree, how many apple trees and how many avocado trees should be planted? What is the corresponding optimal profit? 6. If the profit obtained from each avocado tree increases from $7000 to $15000 and there is no change in the profit for each apple tree, do the optimal values of the decision variables change? Justify your answer 7. If the available fertilizer increases from 1000 tons to 1001 tons, then the optimal profit increases in $500. Mark the right answer. True ( ) False () 8. If the total number of hectares decreases to 199, the optimal profit does not change because the shadow price or dual value is 0. Mark the right answer. True ( ) False ( ) 9. If I avocado tree is planted, What is the corresponding profit? 10. Some employees wish to work overtime. What is the maximum amount, additional to the regular rate, the company would be willing to pay for each overtime hour? Justify your answer. This is the solution and sensitivity report for Problem 6. They were obtained with Solver. 6769LOSSENH 10 11 456 9 10 A A X1 100 15 16 17 18 19 5000 22159 10 6 Variable Cells 7 8 10 $A$2 X1 $B$2 X2 11 12 Constraints 13 14 C B X2 0 7000 20 3 2 50 15 Cell Name Value Cell Name $C$7 Max Z $C$8 Max Z- $C$9 Max Z- $C$10 Max 2 = $C$11 Max Z- D 100 с 0 Max Z= 1000 200 2500 1000 100 2500 1000 E SENSITIVITY REPORT D 0 500000 -500 ***** Final Reduced Objective Allowable

Answer rating: 100% (QA)

1 Number of apple trees to be planted 100 and Number of avocado trees to be planted 0 2 Optimal ... View the full answer