Question 1 Bob Bell's fortieth birthday party promised to be the social event of the year in Cookeville. To prepare, Bob stocked up on the following liquors: LIQUOR AMOUNT ON HAND (millilitres) Bourbon 1 560 Brandy 1 140 Vodka 1 920 Dry vermouth 720 Sweet vermouth 1 080 Bob decides to mix four drinks for the party:

Chaunceys, Sweet Italians, bourbon on the rocks and Russian martinis. A Chauncey consists of 1/4 bourbon, 1/4 vodka, 1/4 brandy and 1/4 sweet vermouth. A Sweet Italian contains 1/4 brandy, 1/2 sweet vermouth, and 1/4 dry vermouth. Bourbon on the rocks contains only bourbon. Finally, a Russian martini consists of 1/3 dry vermouth and 2/3 vodka. Each drink totals 120ml. This means that, taking Russian martini as an example, the drink consists of 40ml dry vermouth and 80ml vodka. Bob's objective is to mix these ingredients in such a way as to maximise the number of drinks in advance.

1.1 Define the decision variables clearly.

1.2 Compile a table showing the five liquor composition (ml) of each of the four different drink mixes.

1.3 Formulate Bob's problem as a linear programming (LP) problem.

1.4 Solve the problem using QM for Windows or Excel QM and clearly state the resulting optimal solution.

1.5 Use the ranging table only, and determine if Bob will use all of his resources to their limit. Substantiate your answer.