Exam 19: Linear Programming

Scenario D.1 Lisa lives out in the country with her seven cats and avoids driving into the big city as much as possible.She has decided to make her own cat food and has the following nutritional guidelines.Each four ounce portion must contain 20 units of protein,15 units of vitamin A,and 10 units of vitamin B.She has eggs,tomatoes,and chicken meat as possible inputs to her cat food.Each ounce of eggs contains 5 units of protein,4 units of Vitamin A,and 3 units of Vitamin B.Each ounce of tomatoes contains 1 unit of protein,5 units of Vitamin A,and 14 units of Vitamin B.Each ounce of chicken contains 22 units of protein,14 units of Vitamin A,and 5 units of Vitamin B.Chicken costs 40 cents per ounce,tomatoes cost 8 cents per ounce,and eggs cost 12 cents per ounce. -Referring to Scenario D.1,what is an appropriate constraint for this scenario?

Table D.3 The Harper Company is in the process of production planning for the next four quarters.The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand.Anticipation inventory is also allowed,but not backorders.Undertime is paid,at a rate of $5.00 per unit.The beginning (or current)inventory is 25 units.Details are shown in the following POM for Windows table. -Use the information in Table D.3.Given the information in the optimal tableau,what is the subcontracting cost,in dollars per unit?

The terms slack and surplus both refer to having too much of a resource.

Consider a corner point to a linear programming problem,which lies at the intersection of the following two constraints: 6X1 + 15X2 < 390 2X1 + X2 < 50 Which of the following statements about the corner point is TRUE?

What are the limitations of the graphical method of linear programming?

The objective function Maximize Z = 3x2 + 4y is appropriate for linear programming.

The interval over which the right-hand-side parameter of a constraint can vary while its shadow price remains valid is the ________.

What is degeneracy in the context of linear programming? Why is degeneracy a concern?

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is CORRECT?

For an "equal" constraint,only points ________ are feasible solutions.

In linear programming,a(n)________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

Only corner points should be considered for the optimal solution to a linear programming problem.

________ occurs in a linear programming problem when the number of nonzero variables in the optimal solution is fewer than the number of constraints.

What are the assumptions of linear programming? Provide examples of each.

Decision variables are represented in both the objective function and the constraints while formulating a linear program.

The assumption of ________ allows a decision maker to combine the profit from one product with the profit from another to realize the total profit from a feasible solution.

Table D.3 The Harper Company is in the process of production planning for the next four quarters.The company follows a policy of a stable workforce and uses overtime and subcontracting to meet uneven forecasted demand.Anticipation inventory is also allowed,but not backorders.Undertime is paid,at a rate of $5.00 per unit.The beginning (or current)inventory is 25 units.Details are shown in the following POM for Windows table. -Use the information in Table D.3.According to the optimal production plan,what is the total ending inventory in the second quarter? Assume that the plan that uses the least amount of subcontracting is used.

An equality constraint requires that only the points on the line described by the constraint are feasible.

The CZ Jewelry Company produces two products: (1)engagement rings and (2)jeweled watches.The production process for each is similar in that both require a certain number of hours of diamond work and a certain number of labor hours in the gold department.Each ring takes four hours of diamond work and two hours in the gold shop.Each watch requires three hours in diamonds and one hour in the gold department.There are 240 hours of diamond labor available and 100 hours of gold department time available for the next month.Each engagement ring sold yields a profit of $9;each watch produced may be sold for a $10 profit. a.Give a complete formulation of this problem,including a careful definition of your decision variables.Let the first decision variable, (X1),deal with rings,the second decision variable, (X2),with watches,the first constraint with diamonds,and the second constraint with gold. b.Graph the problem fully in the following space.Label the axes carefully,plot the constraints,shade the feasibility region,plot at least one isoprofit line that reveals the optimal solution,circle the corner points and highlight the optimal corner point so found,and solve for it algebraically.(Show all your work to get credit. )

A manufacturer builds finished items A,B,and C from five different components.They currently have several finished units,a number of items that are partially complete,and many components that have just been delivered from their suppliers.The finished items,incomplete items and raw components can all be assigned some monetary value even though the manufacturer typically does not sell anything except finished items.The manufacturer needs to raise capital quickly so they formulate a linear program to help them decide on the most profitable way ahead.Their linear programming expert forgets to restrict their decision variables to non-negative values and is surprised when the computer output tells them that finished item A and C should be negative.If the company always follows the advice of their linear programming analysis,what should they do and why?