Exam 2: Linear Programming: Model Formulation and Graphical Solution

All linear programming models exhibit a set of constraints.

Corner points on the boundary of the feasible solution area are called ________ points.

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. -Which of the following constraints has a surplus greater than 0?

The ________ is a linear relationship reflecting the objective of an operation.

The ________ step in formulating a linear programming model is to define the decision variables.

The following equation represents a resource constraint for a maximization problem: X + Y ≥ 20.

The production manager for the Coory soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What are the optimal daily production quantities of each product and the optimal daily profit?

The terms in the objective function or constraints are multiplicative.

If the objective function is parallel to a constraint, the constraint is infeasible.

Consider the following linear program: MAX Z = 60A + 50B s.t.  10A + 20B ? 200    8A + 5B ? 80    A ? 2    B ? 5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

The terms in the objective function or constraints are additive.

In a constraint, the ________ variable represents unused resources.

A graphical solution is limited to solving linear programming problems with ________ decision variables

The equation 8xy = 32 satisfies the proportionality property of linear programming.

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. -Which line is represented by the equation 2X + Y ≥ 8?

Without satisfying the non-negativity constraint, a solution that satisfies all the other constraints of a linear programming problem is called

Solve the following graphically: Max z = 3x1 + 4x2 s.t.   x1 + 2x2 ?16    2x1 + 3x2 ? 18    x1 ? 2    x2 ? 10    x1, x2 ? 0 What are the optimal values of x1, x2, and z?

Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. Which of the following is not a feasible purchase combination?

A linear programming model consists of only decision variables and constraints.

Consider the following maximization problem. MAX z = x + 2y S .t.    2x + 3y ? 6    5x + 6y ? 30        Y ? 1 The optimal solution