Exam 2: Introduction to Management Science Models

The Carolina Chemical Company (CCC) makes two products, soap and shampoo, both in liquid form.The same two raw material inputs, glycerin and potash, and the same production line are used in the manufacture of each.Each production day, one ton of glycerin and two tons of potash are available.Each gallon of soap requires 8 pounds of glycerin and 32 pounds of potash, while a gallon of shampoo uses 12 pounds of glycerin and 19 pounds of potash. CCC's production day is 8 full hours (480 minutes).Its production line can turn out 25 gallons of soap, or 20 gallons of shampoo, per hour.Only one product can be made at a time, but the line is easily changed over at negligible cost from one item to the other.Forecasts indicate that demand for soap and shampoo far exceeds production capacity.The profit per gallon of soap is $30 and per gallon of shampoo is $36. A.Formulate a linear programming model that will maximize CCC's daily profit. B.Suppose that the production of soap also yields a byproduct called Blyx.The manufacturing process yields 0.3 units of Blyx for every unit of soap.Up to 15 gallons of Blyx can be sold per day for canine shampoo at a profit of $10 per gallon.CCC must dispose of any excess of Blyx at a removal cost of $4 per gallon.Using X3 = the number of gallons of Blyx produced up to 15 gallons, and X4 = the number of gallons of Blyx produced over 15 gallons, modify the linear programming model for this problem.

An optimal solution must have no slack on at least one constraint.

Squire Leathers produces two sizes of wallets from cowhide.The first requires 60 squire inches of cowhide and the second requires 100 square inches.The company has 1000 square feet of cowhide.Part of the model is:

An extreme point is an optimal solution.

Jungle Figures, Inc.produces two models of its stuffed giraffes, which it markets to high-end retail stores.The large giraffe requires 2 pounds of stuffing material and 6 minutes of machine time.The small giraffe requires 1 pound of stuffing material and 12 minutes of machine time since its tighter stitching pattern requires it to be stitched twice.There are 800 pounds of stuffing and 70 machine hours available each week.By adhering to a policy of not producing more than twice the number of large giraffes as small giraffes (this is a constraint), Jungle Figures has been able to sell all the giraffes it produces at $12 per large giraffe and $9 per small giraffe.

The feasible region does not include:

If two extreme points are optimal, then so is every point on the line segment connecting the two extreme points.

"Range of optimality" describes the impact of simultaneous changes in objective function values and right-hand-side values.

Office2000 produces expensive, quality 2-drawer and 4-drawer filing cabinets from solid oak for major corporations.A 2-drawer model utilizes 2 labor hours to produce and package for a net profit of $75.The 4-drawer model utilizes 3 labor hours to produce and package and nets a profit of $125.Each month Office2000 has 360 labor hours available and can obtain up to 200 2-drawer frames, 200 4-drawer frames, and 400 drawers from its oak supplier.

A small foundry has received an order for an iron alloy called Falloy which has the following specifications: Content Specification Nickel 5\% Manganese 4\% Copper 1-2\% Impurities no more than 3\% Iron the balance Falloy can be produced from the following inputs (balance to 100% consisting of iron). Content Specification Nickel 5\% Manganese 4\% Copper 1-2\% Impurities no more than 3\% Iron the balance Formulate the linear programming problem that will indicate the blending "recipe" that will minimize the cost of this alloy.

What is wrong with this linear programming model?

When compared with standard linear programming, integer linear programming typically has:

The principle of "complementary slackness" implies that:

Define the additivity assumption.

A non-binding constraint is always a redundant constraint.

Which statement is not true if a maximization problem has an unbounded solution?

Explain the SUMPRODUCT function of Excel.

In the branch-and-bound technique for solving integer linear programming models with a maximization objective function:

Linear programming and integer linear programming both yield a great amount of sensitivity analysis.

A linear programming problem with all " $\le$ " functional constraints and nonnegative right hand side values will never be infeasible.