Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beerYodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is shown in table below. The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely.Bettywantstodecide on thenumberofgallonsofeachbrandofbeertoordersoastomake the most profit. Formulate a linear programming model for this problem. Define x₁ as the number of gallons of Yodel to order, x₂ as the number of gallons of Shotz to order, x₃ as the number of gallons of Rainwater to order, and Z as the total profit.

a. According to Excels sensitivity report for the previous formulated model (Eagle Tavern), the shadow price for the capacity constraint is

0

1.25

1.5

1.6

b. According to Excels sensitivity report for the previous formulated model (Eagle Tavern), which of the following statement is correct regarding the shadow price of budget constraint?

The shadow price for budget constraint is $.25

Increasing current budget does NOT result in profit increase for the tavern

The shadow price of $.25 is only valid when the taverns budget is between [$1100, +infinity]

The shadow price is zero because the tavern has used up all of its current budget

c. According to Excels sensitivity report for the previous formulated model (Eagle Tavern), the sensitivity range for the objective function coefficient of x3 (or Rainwater) is

[1.25, +infinity]

[1.5, +infinity]

[-infinity, 1.5]

[-infinity, 1.25]

d. According to Excels sensitivity report for the previous formulated model (Eagle Tavern), which of the following statement is false?

As long as the profit for each gallon of Yodel at the tavern is $1.25 or above, the optimal solution remains the same for the tavern

As long as the profit for each gallon of Shotz at the tavern is $1.25 or above, the optimal solution remains the same for the tavern

As long as the profit for each gallon of Rainwater at the tavern is $1.5 or below, the optimal solution remains the same for the tavern

As long as the storage capacity of the tavern is no more than 900 gallons, the optimal solution would suggest the tavern to offer all three brands of beer