HALLER’S PUB & BREWERY Jeremy Haller of Haller’s Pub & Brewery, described in the

Question

HALLER’S PUB & BREWERY Jeremy Haller of Haller’s Pub & Brewery, described in the opening episode, has compiled data describing the amount of different ingredients and labor resources needed to brew the six different types of beers that the brewery makes. He also gathered financial information and estimated demand over a 26-week forecast horizon. These data are shown in Exhibit C.24. The profits for each batch of each type of beer are Light Ale: $3,925.78 Golden Ale: $4,062.75 Freedom Wheat: $3,732.34 Berry Wheat: $3,704.49 Dark Ale: $3,905.79 Hearty Stout: $3,490.22 These values incorporate fixed overhead costs of $7,500 per batch. a. Use the data in Exhibit C.19 to validate the profit figures. b. How many batches should Haller plan to make of each product? Develop and solve an LP model. c. In the brewing business, the price of grain and hops fluctuates fairly regularly. Examine the effect of a 10 percent increase in the price of all grains and hops on the optimal solution. d. Customer demand for beer at Haller’s, especially during holiday months and economic slowdowns, has a tendency to fluctuate just as the price of grains and hops. Examine the effect of a 10 percent decrease in overall customer demand. e. Due to a shrinking interest in Stout beer, Haller’s would like to understand the effect on profitability of removing it from its product line. Assume that all Stout beer drinkers would be lost with the elimination of the beer (that is, they do not switch to another type of beer). Summarize all your results in a memo to Jeremy Haller

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on page C29-C30

Explanation / Answer

a. Profit figures are validated by calculating the variables costs for each type of final product. Revenue per batch irrespective of type of finished product is $13,050 (3*4350) and fixed cost of $7,500.

Profit = Revenue - fixed cost - variable cost

Decision variables are the number of batches of each type of final products denoted by L for Light Ale, G for Golden Ale and so on F, B, D and H for other four types of final products.

Objective function is to maximize Total Profit given as:

     Maximize    3925.78L + 4062.75G + 3732.34F + 3704.49B + 3905.79D + 3490.22H

Constraints are related to availabilities of the raw materials as mentioned in the above tables

Number of batches can not be negative therefore non-negativity constraint that is L, G, F, B, D, H >= 0

Raw Materials quantities matrix L G F B D H Availability Cost per unit A2 525 400 375 350 450 375 30000 0.35 A6 125 125 150 250 225 8000 0.4 Ac 175 175 5000 0.42 Gv 125 200 175 50 5000 0.45 Fb 75 150 150 75 5000 0.47 Ldm 35 45 50 25 2000 0.37 Hh 4 3 2 2 8 500 0.32 Kh 1 4 4 500 0.29 Th 4 2 2 4 2 500 0.31 Bl 70 72 81 83 75 96 4032 18

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