Exam 4: Linear Programming

The graph of the feasible region for a mixture problem is shown below. Find the point that maximizes the profit function P = 2x + y.

What type of solution does the Northwest Corner Rule produce for the transportation problem?

Find the point of intersection for the lines represented by the equations 2x + 4y = 12 and 3x + y = 13.

Write the resource constraints for this situation: Kim and Lynn produce tables (x) and chairs (y). Each piece is assembled, sanded, and stained. A table requires two hours to assemble, three hours to sand, and three hours to stain. A chair requires four hours to assemble, two hours to sand, and three hours to stain. The profit earned on each table is $20 and on each chair is $12. Together Kim and Lynn spend at most 16 hours assembling, 10 hours sanding, and 13 hours staining.

An optimal solution for a linear programming problem will always occur at a corner point of the feasible region.

The feasible region for a linear programming mixture problem with two products is in the first quadrant of the Cartesian plane.

Given below is the sketch of the feasible region in a linear programming problem. Which point is NOT in the feasible region?

Suppose the feasible region has five corners, at these points: (1, 1), (1, 7), (5, 7), (5, 5), and (4, 3). If the profit formula is P = $5x  $2y, which point maximizes the profit?

The feasible region for a linear programming mixture problem may have holes in it.

Graph the feasible region identified by the inequalities: 2x+3y\leq12 1x+5y\leq10 x\geq0,y\geq0

Any linear programming problem has at most two products.

Find the point of intersection for the lines represented by the equations 3x + 2y = 14 and 4x + 5y = 28.

Sketch the graph of the inequality 4x + 6y  12.

Use the following to answer the Questions: concern the following tableau for a shipping problem. -In the optimal solution, how many units are shipped from supplier I to customer 2?

Refer to the feasible region defined by the following constraints to answer the following questions : x+y\leq6 x+2y\leq8 x\geq0 y\geq0 -If the profit formula is $P = 5 x$ what is the maximum profit?

Suppose the feasible region has four corners, at these points: (0, 0), (8, 0), (0, 12), and (4, 8). For which of these profit formulas is the profit maximized, producing a mix of products at (4, 8)?

Use the following tableau to answer the questions: concern the following tableau for a shipping problem. -What is the cost for the optimal solution to this shipping problem?

Describe a mixture problem.

Given below is the sketch of the feasible region in a linear programming problem. Which point is NOT in the feasible region?

Write a profit formula for this mixture problem: A company manufactures patio chairs (x) and rockers (y). Each piece is made of wood, plastic, and aluminum. A chair requires one unit of wood, one unit of plastic, and two units of aluminum. A rocker requires one unit of wood, two units of plastic, and five units of aluminum. The company's profit on a chair is $7 and on a rocker is $12. The company has available 400 units of wood, 500 units of plastic, and 1450 units of aluminum.