Oliver Winery produces four award-winning wines in Bloomington. Indiana. The profit contribution, labor hours, and tank usage (in hours) per gallon for each type of wine are given in the table below. By law, at most 100.000 gallons of wine can be produced each year. A maximum of 12.000 labor hours and 32.000 tank hours are available annually. Each gallon of wine I spends an average of 1/3 year in inventory: wine 2. an average of I year: sine 3. an average of 2 years; wine 4. 311 average of 10/3 years. The winers's warehouse can handle an avenge inventory level of 50.000 gallons.

a. Develop an LP model to determine how much of each type of wine should be produced all) to maximize Oliver Winery's profit.

b. Solve the model using Excel Solver. What is the optimal solution?

c. If the profit per gallon for type 2 wine is decreased to I I. does the optimal solution change? Why?

d. What is the shadow price for the inventory constraint? What does it mean?

e. What is the reduced cost for the decision variable defining the gallons of type 4 wine produced annually? What does it mean?

Wine 1 2 3 Profit (S) 6 12 20 30 Labor (Hr) .2 .3 .3 .5 Tank (Hr) .5 .5 1 1.5