Linear Programming Graphical Method Quiz

A feasible solution is one that satisfies all the constraints of a linear programming problem simultaneously.

• true

• false

The best feasible solution is called the optimal solution.

• true

• false

The graphical method can handle problems that involve any number of decision variables.

• true

• false

An objective function represents a family of parallel lines.

• true

• false

If a single optimal solution exists while using the graphical method to solve a linear programming problem, it will exist at a corner point.

• true

• false

When solving a minimization problem graphically, it is generally the goal to move the objective function line out, away from the origin, as far as possible.

• true

• false

When using the graphical method, the region that satisfies all of the constraints of a linear programming problem is called the:

• optimum solution space

• region of optimality

• profit maximization space

• feasible region

• region of nonnegativity

Solving linear programming problems graphically

• is possible with any number of decision variables.

• provides geometric intuition about what linear programming is trying to achieve.

• will always result in an optimal solution.

• All of the answer choices are correct.

• None of the answer choices are correct.

The production planner for Fine Coffees produces two coffee blends: American (A) and British (B). He can only get 300 pounds of Colombian beans per week and 200 pounds of Dominican beans per week. Each pound of American blend coffee requires 12 ounces of Colombian beans and 4 ounces of Dominican beans, while a pound of British blend coffee uses 8 ounces of each type of bean. Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound. The goal of Fine Coffees is to maximize profits. Which of the following is not a feasible solution?

• (A, B) = (0, 0)

• (A, B) = (0, 400)

• (A, B) = (200, 300)

• (A, B) = (400, 0)

• (A, B) = (400, 400)

A local bagel shop produces bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's baking. Bagel profits are 20 cents each and croissant profits are 30 cents each. The shop wishes to maximize profits. Which of the following is not a feasible solution?

• (B, C) = (0, 0)

• (B, C) = (0, 1100)

• (B, C) = (800, 600)

• (B, C) = (1100, 0)

• (B, C) = (0, 1400)