A French vineyard in the Chablis region uses Chardonnay grapes to make Chardonnay wine and Blanc de
Question:
A French vineyard in the Chablis region uses Chardonnay grapes to make Chardonnay wine and Blanc de Blancs blended champagne. To produce 1 liter of wine, the vineyard uses about 8 kilograms of Chardonnay grapes, and the winemakers usually spend about 2.5 hours in the winemaking process, including pressing, blending, and processing. To produce 1 liter of Blanc de Blancs champagne, about 6 kilograms of Chardonnay grapes are used, with the pressing, blending, and processing time of 3 hours. A liter of Chardonnay from the vineyard is usually sold at $55, and each liter of champagne is sold at $45. Each week, 400 kilograms of Chardonnay grapes and 150 hours for pressing, blending, and processing are available.
a. Formulate and solve the LP model that maximizes revenue given the constraints. What is the maximum revenue that the vineyard can make from selling Chardonnay wine and champagne? How many liters of Chardonnay wine and champagne should the vineyard make each week?
b. If the amount of Chardonnay grapes available to the vineyard increases to 500 kilograms per week, how much wine and champagne should be made? Explain.
c. If the price of champagne drops to $30 per liter, how much wine and champagne should the vineyard make? Explain and discuss your answer.
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