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Vicky’s Breweries produces beer and ale. Beer sells for $5 per barrel, and ale

sells for $2 per barrel. Producing a barrel of beer requires 5 pounds of corn

and 2 pounds of hops. Producing a barrel of ale requires 2 pounds of corn and

1 pounds of hops. Sixty pounds of corn and 25 pounds of hops are available.

Formulate a Linear Program (LP) that can be used to maximize the revenue.

Solve the LP graphically.

Question 2

True or false? Explain if true or provide counter examples if false. (Don’t get

too carried away – a short paragraph for each is good enough. ;-))

a. For an LP optimal value to be unbounded, the LP feasible region must

be unbounded.

b. Every LP with an unbounded feasible region has an unbounded

optimal solution.

Question 3

Can you think of a reason why we don’t allow an LP to have “<” or “>”

constraints? (Again: a concise answer would be nice).

Question 4

Vicky’s Perfume Company uses Chemicals A and B to produce two perfumes.

Spellbound must be at least 70% Chemical A, and Bewitched must be at least

60% Chemical B. Up to 40 oz of Spellbound can be sold at $6 per oz; up to 30

oz of Bewitched can be sold at $5 per oz. Up to 45 oz of Chemical A can be

purchased at $6 per oz, and up to 40 oz of Chemical B can be purchased at $4

per oz. Formulate an LP that can be used to maximize Vicky’s profits.

PART 2

Question 5

Find the feasible region for the following LP graphically. Solve the LP using

the Simplex Algorithm, and mark the points that represent the sequence of

basic feasible solutions obtained at each step.

Question 6

Consider the following set of constraints, assuming that

Perform Phase I of the Two-phase method, until either the LP is proven

infeasible, or a feasible solution to the LP is obtained.

a. Maximize: z = 5x1 + 6x2,

Subject to constraints (1), (3), and (4).

b. Minimize: z = 4x1 + 6x2,

Subject to constraints (1), (2) and (5)

SIT399 Advanced Topics in Mathematics

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