Thendral Krishnan (TK) is the co-founder and CEO of Great Western Vineyard (GWV), a vineyard established...

  

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Thendral Krishnan (TK) is the co-founder and CEO of Great Western Vineyard (GWV), a vineyard established in Thekkady, Kerala. GWV cultivates three types of grapes, namely, (a) Malbec, (b) Cabernet, and (c) Riesling. The monthly production of Malbec, Cabernet, and Riesling at GWV is 350 kg, 300 kg, and 200 kg, respectively. Using these grapes, Thendral Krishnan makes three brands of wines, namely, (a) Chardonnay, (b) Blanc, and (c) Riesling W. The wines are made by mixing the three different types of grapes and two additives at various proportions. The amount of grapes and additives used to produce one litre of different brands of wines are shown in table: Grapes Amount in kg Used Malbec Cabernet Riesling 0.75 1.25 0.15 0.8 1.8 0.25 Riesling W 0.4 0.6 2 Availability 350 300 200 Wine Chardonnay Blanc Additives used in kg Additive 1 Additive 2 0.1 0.2 0.05 0.15 0.08 0.12 120 80 The profit earned from wines Chardonnay, Blanc, and Riesling W is 400, 950, and 1350 per 1 litre, respectively. The following LP formulation is written to maximize the profit. Monthly maximum demand for Chardonnay, Blanc, and Riesling W is 1000, 750, and 250 respectively. Let X₁ = Amount (in litres) of Chardonnay produced = Amount (in litres) of Blanc produced X, = Amount (in litres) of Riesling W produced The objective is Max 400X, +950X, +1350X, Subject to 1.25X, +0.80X₂ +0.40X, ≤350 0.75X, +1.80X₂ +0.60X, ≤300 0.15X, +0.25X₂ +2.00X, ≤200 0.10X, +0.05X, +0.08.X, <120 0.20X, +0.15X₂ +0.12X, 80 X₁ ≤1000 X₂ X₁, X₂, X, 20 The sensitivity report output is provided below: $750 X, ≤250 Variable Cells Cell $B$5 $C$5 $D$5 Constraint 1 2 3 4 5 6 7 8 Name X1 Constraints Final Value 0 X2 139.1304348 X3 82.60869565 Final Value 144.3478261 300 200 13.56521739 30.7826087 0 139.1304348 82.60869565 Reduced Cost -20.54347826 0 0 Shadow Price 0 452.8985507 539.1304348 0 0 0 0 0 Objective Allowable Coefficient Increase 400 -950 1350 Constraint R.H. Side 350 300 200 120 80 1000 750 250 20.54347826 3100 6250 Allowable Allowable Increase Decrease 1E+30 205.6521739 473 240 320.8333333 158.3333333 106.4347826 49.2173913 1000 610.8695652 167.3913043 1E+30 1E+30 Allowable Decrease 1E+30 50.26595745 859.0909091 IE+30 IE+30 1E+30 Based on the provided information, answer the following questions. a) What is the value of the objective function at optimality? b) A loyal customer of TK has asked for 20 litres of Chardonnay wine. What will be the impact on profit for GWV if TK decides to supply Chardonnay wine? TK would like to ensure that supplying Chardonnay will not impact the profitability of GWV. What will be your suggestion? [CLO 2, 3 Mark] [CLO 2, 1 Mark] c) In addition to producing on its own, TK can procure Malbec from Bangalore. Should he procure it? [CLO 2, 2 Mark] d) The supplier of Cabernet grapes from Bangalore is ready to provide an additional quantity of 400 Kg as requested for Rs. 480 per Kg. Should TK buy 400 kg from Bangalore supplier? Justify your answer. [CLO 2, 2 Mark] e) The grape Malbec can be directly sold in market at 70 RS per kg instead of using them in wine production. What will be your suggestion? If yes, then what quantity of Malbec grape can be sold in market? [CLO 2, 1 Mark] f) Due to Reisling crop failure in Nappa county, the demand for Reisling W increases significantly. TK decided to increase profit on Reisling W to 3500 Rs. What will be the impact on optimal solution? [CLO 2, 1 Mark] Thendral Krishnan (TK) is the co-founder and CEO of Great Western Vineyard (GWV), a vineyard established in Thekkady, Kerala. GWV cultivates three types of grapes, namely, (a) Malbec, (b) Cabernet, and (c) Riesling. The monthly production of Malbec, Cabernet, and Riesling at GWV is 350 kg, 300 kg, and 200 kg, respectively. Using these grapes, Thendral Krishnan makes three brands of wines, namely, (a) Chardonnay, (b) Blanc, and (c) Riesling W. The wines are made by mixing the three different types of grapes and two additives at various proportions. The amount of grapes and additives used to produce one litre of different brands of wines are shown in table: Grapes Amount in kg Used Malbec Cabernet Riesling 0.75 1.25 0.15 0.8 1.8 0.25 Riesling W 0.4 0.6 2 Availability 350 300 200 Wine Chardonnay Blanc Additives used in kg Additive 1 Additive 2 0.1 0.2 0.05 0.15 0.08 0.12 120 80 The profit earned from wines Chardonnay, Blanc, and Riesling W is 400, 950, and 1350 per 1 litre, respectively. The following LP formulation is written to maximize the profit. Monthly maximum demand for Chardonnay, Blanc, and Riesling W is 1000, 750, and 250 respectively. Let X₁ = Amount (in litres) of Chardonnay produced = Amount (in litres) of Blanc produced X, = Amount (in litres) of Riesling W produced The objective is Max 400X, +950X, +1350X, Subject to 1.25X, +0.80X₂ +0.40X, ≤350 0.75X, +1.80X₂ +0.60X, ≤300 0.15X, +0.25X₂ +2.00X, ≤200 0.10X, +0.05X, +0.08.X, <120 0.20X, +0.15X₂ +0.12X, 80 X₁ ≤1000 X₂ X₁, X₂, X, 20 The sensitivity report output is provided below: $750 X, ≤250 Variable Cells Cell $B$5 $C$5 $D$5 Constraint 1 2 3 4 5 6 7 8 Name X1 Constraints Final Value 0 X2 139.1304348 X3 82.60869565 Final Value 144.3478261 300 200 13.56521739 30.7826087 0 139.1304348 82.60869565 Reduced Cost -20.54347826 0 0 Shadow Price 0 452.8985507 539.1304348 0 0 0 0 0 Objective Allowable Coefficient Increase 400 -950 1350 Constraint R.H. Side 350 300 200 120 80 1000 750 250 20.54347826 3100 6250 Allowable Allowable Increase Decrease 1E+30 205.6521739 473 240 320.8333333 158.3333333 106.4347826 49.2173913 1000 610.8695652 167.3913043 1E+30 1E+30 Allowable Decrease 1E+30 50.26595745 859.0909091 IE+30 IE+30 1E+30 Based on the provided information, answer the following questions. a) What is the value of the objective function at optimality? b) A loyal customer of TK has asked for 20 litres of Chardonnay wine. What will be the impact on profit for GWV if TK decides to supply Chardonnay wine? TK would like to ensure that supplying Chardonnay will not impact the profitability of GWV. What will be your suggestion? [CLO 2, 3 Mark] [CLO 2, 1 Mark] c) In addition to producing on its own, TK can procure Malbec from Bangalore. Should he procure it? [CLO 2, 2 Mark] d) The supplier of Cabernet grapes from Bangalore is ready to provide an additional quantity of 400 Kg as requested for Rs. 480 per Kg. Should TK buy 400 kg from Bangalore supplier? Justify your answer. [CLO 2, 2 Mark] e) The grape Malbec can be directly sold in market at 70 RS per kg instead of using them in wine production. What will be your suggestion? If yes, then what quantity of Malbec grape can be sold in market? [CLO 2, 1 Mark] f) Due to Reisling crop failure in Nappa county, the demand for Reisling W increases significantly. TK decided to increase profit on Reisling W to 3500 Rs. What will be the impact on optimal solution? [CLO 2, 1 Mark]

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The LPP formulation and sensitivity report is provided The sensitivity report provides the final values for the decision variables and LHS value of constraints It also provides the impact of changes i... View the full answer