Exam 13: Introduction to Optimization Modeling

When using the graphical solution method to solve linear programming problems,the set of points that satisfy all constraints is called the:

When formulating a linear programming spreadsheet model,there is a set of designated cells that play the role of the decision variables.These are called the objective cells.

(A)Verify that Mary should purchase 12 units of food 2 each day and thus oversatisfy the vitamin C requirement by 6 units. (B)Mary's husband has put his foot down and demanded that Mary fulfill the family's daily nutritional requirement exactly by obtaining precisely 12 units of vitamin A and 6 units of vitamin C.The optimal solution to the new problem will involve ingesting less vitamin C,but it will be more expensive,why? (C)Starting with the optimal solution to (B),use the SloverTable add-in to see what happens to the total cost when the vitamin A and vitamin C requirements both vary (independently)from 3 to 18 in 3-unit increments.That is,from a two-way table.Describe the behavior you observe.In particular,are the changes in total cost the same as you look across each row of the table? Are they the same as you look across each column of the table?

The divisibility property of LP models simply means that we allow only integer levels of the activities.

What is the objective function in this problem?

The term nonnegativity refers to the condition where:

The set of all values of the changing cells that satisfy all constraints,not including the nonnegativity constraints,is called the feasible region.

When there is a problem with Solver being able to find a solution,many times it is an indication of a (n):

If an LP model does have an unbounded solution,then we must have made a mistake - either we made an input error or we omitted one or more constraints.

Unboundedness refers to the situation in which the LP model has been formulated in such a way that the objective function is unbounded - that is,it can be made as large (for maximization problems)or as small (for minimization problems)as we like.

Shadow prices are associated with nonbinding constraints,and show the change in the optimal objective function value when the right side of the constraint equation changes by one unit.

The optimal solution to any linear programming model is:

The optimal solution to any linear programming model is a corner point of a polygon.

(A)Find an optimal solution to the problem.What is the production plan,and what is the total revenue? (B)Obtain a sensitivity report for the solution reported in (A).Which constraints are binding? (C)What is the incremental contribution associated with adding an hour of assembly time? Over what range of increase is the marginal value valid? (D)What is the value of additional capacity on the polisher? How much increase and decrease in this capacity is possible before a change occurs in the optimal production schedule? (E)An advertising agency has devised a marketing plan for the Valley Chassis Company that will increase the market for Deluxe chassis.The plan will increase demand by 75 Deluxe chassis per month at a cost of $100 per month.Should Valley adopt the plan? Briefly explain why. (F)Suppose that four more hours of chassis assembly time could be made available.How much would profit change? (G)Suppose next that Valley's marketing department proposes lowering the price for a standard chassis from $12 to $11.50 so that more can be sold (since there is slack under the demand constraint).Would the optimal solution change? Explain why,or why not. (H)If Valley could obtain 1,000 pounds more of raw material (steel or aluminum),which should it procure? How much should they be willing to pay per pound for the steel or aluminum? Explain your answer. (I)In doing some contingency planning,Valley thinks that the aging stamping machine will soon need to be taken down for repairs that could last 2 months and will cost $10,000.During that time,they can continue to operate by outsourcing the stamping at $2.50 per chassis (deluxe or standard),although the capacity will be reduced from 2,500 to 1,500.What will be the total cost to repair the stamping machine?

Consider the following linear programming problem: Minimize Subject to The above linear programming problem:

In using Excel to solve linear programming problems,the target cell represents the:

In determining the optimal solution to a linear programming problem graphically,if the objective is to maximize the objective,we pull the objective function line down until it contacts the feasible region.

In linear programming,sensitivity analysis involves examining how sensitive the optimal solution is to changes in:

Linear programming problems can always be formulated algebraically,but not always on spreadsheet.

The feasible region in a graphical solution of a linear programming problem will appear as some type of polygon,with lines forming all sides.