Q2. Selen is arranging a graduation party. She is expecting 120 guests to her party and...

Transcribed Image Text:

Q2. Selen is arranging a graduation party. She is expecting 120 guests to her party and she will make delicacies for them. Selen has decided to make only 3 kinds of delicacies: cake, cookies, and buns (a cake is enough for 10 people, a cookie for one person, and a batch of buns for 20 people). The LP formulation to minimize the total cost of preparing the delicacies and the corresponding Excel Sensitivity Report are provided below. Decision Variables: X = number of cakes Y = number of cookies Z = number of bun batches Minimize Costs ($) = 10X + 4Y + 15Z subject to 10X + Y + 20Z ≥ 120 10X ≥ 2Y 30X + Y + 40Z ≤ 600 10X ≥ 20 Y ≥ 20 20Z ≥ 20 X, Y, Z ≥ 0. (min. required demand) (min. required ratio of number of cakes to number of cookies) (available preparation time) (min. requirement for cakes) (min. requirement for cookies) (min. requirement for bun batches) (nonnegativity constraint) Cell $C$3 number of cakes $D$3 number of cookies $E$3 number of bun batches Name Cell $F$6 min. required demand $F$7 min. required ratio of number of cakes to number of cookies $F$8 available preparation time Name $F$9 min. requirement for cakes $F$10 min. requirement for cookies $F$11 min. requirement for bun batches Final Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease Value 4 20 3 0 0 0 10 4 15 0.75 0.25 0 0 3.75 0 1E+30 1E+30 5 Final Shadow Constraint Allowable Allowable Value Price 120 R.H. Side Increase Decrease 0 260 40 20 60 120 0 600 20 20 20 2.5 3.75 15 170 40 1E+30 20 13.33 40 40 20 340 1E+30 10 1E+30 Answer the following questions by showing all your calculations clearly: a. What is the impact on total cost if we increase the min. required demand to 150 units? b. What is the impact on total cost if we decrease the available preparation time by 250 units? c. If the objective function coefficient of cakes decreases by 5 units, will the optimal solution change? What about the value of the objective function? d. If the objective function coefficient of bun batches increases by 3 units, will the optimal solution change? What about the value of the objective function? e. We can increase the right-hand-side of the min. requirement for cookies constraint by 5 units, while decreasing the right-hand-side of the min. required demand constraint by 20 units. Is it worth the effort? Find the impact on total cost. Q2. Selen is arranging a graduation party. She is expecting 120 guests to her party and she will make delicacies for them. Selen has decided to make only 3 kinds of delicacies: cake, cookies, and buns (a cake is enough for 10 people, a cookie for one person, and a batch of buns for 20 people). The LP formulation to minimize the total cost of preparing the delicacies and the corresponding Excel Sensitivity Report are provided below. Decision Variables: X = number of cakes Y = number of cookies Z = number of bun batches Minimize Costs ($) = 10X + 4Y + 15Z subject to 10X + Y + 20Z ≥ 120 10X ≥ 2Y 30X + Y + 40Z ≤ 600 10X ≥ 20 Y ≥ 20 20Z ≥ 20 X, Y, Z ≥ 0. (min. required demand) (min. required ratio of number of cakes to number of cookies) (available preparation time) (min. requirement for cakes) (min. requirement for cookies) (min. requirement for bun batches) (nonnegativity constraint) Cell $C$3 number of cakes $D$3 number of cookies $E$3 number of bun batches Name Cell $F$6 min. required demand $F$7 min. required ratio of number of cakes to number of cookies $F$8 available preparation time Name $F$9 min. requirement for cakes $F$10 min. requirement for cookies $F$11 min. requirement for bun batches Final Reduced Objective Allowable Allowable Cost Coefficient Increase Decrease Value 4 20 3 0 0 0 10 4 15 0.75 0.25 0 0 3.75 0 1E+30 1E+30 5 Final Shadow Constraint Allowable Allowable Value Price 120 R.H. Side Increase Decrease 0 260 40 20 60 120 0 600 20 20 20 2.5 3.75 15 170 40 1E+30 20 13.33 40 40 20 340 1E+30 10 1E+30 Answer the following questions by showing all your calculations clearly: a. What is the impact on total cost if we increase the min. required demand to 150 units? b. What is the impact on total cost if we decrease the available preparation time by 250 units? c. If the objective function coefficient of cakes decreases by 5 units, will the optimal solution change? What about the value of the objective function? d. If the objective function coefficient of bun batches increases by 3 units, will the optimal solution change? What about the value of the objective function? e. We can increase the right-hand-side of the min. requirement for cookies constraint by 5 units, while decreasing the right-hand-side of the min. required demand constraint by 20 units. Is it worth the effort? Find the impact on total cost.