Exam 4: Linear Programming: Modeling Examples

In most media selection decisions, the objective of the decision maker is to minimize cost.

When the poultry farmer runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He studies his sensitivity report (copied below) and decides to write a constraint that requires two Cochin chickens to be selected. If the current optimal mix of breeds results in 160 eggs per week, which of the following statements is best?

Data envelopment analysis indicates the relative ________ of a service unit compared with others.

For the production combination of 600 bear claws and 800 almond-filled croissants, how much flour and almond paste are remaining?

A balanced transportation model should have ________ constraints.

Small motors for garden equipment are produced at four manufacturing facilities and need to be shipped to three plants that produce different garden items (lawn mowers, rototillers, leaf blowers). The company wants to minimize the cost of transporting items between the facilities, taking into account the demand at the three different plants, and the supply at each manufacturing site. The table below shows the cost to ship one unit between each manufacturing facility and each plant, as well as the demand at each plant and the supply at each manufacturing facility. $~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\text { To Plant }$ From Manufacturing Facility A B C Supply 1 4 4.5 3.2 200 2 3.5 3 4 200 3 4 3.5 4.25 300 \nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace\nobreakspace Demand 250 150 200 Write the formulation for this problem.

The type of linear program that compares services to indicate which one is less productive or inefficient is called

A croissant shop produces two products: bear claws (B) and almond-filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS (tablespoons) of almond paste. An almond-filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today's production run. The shop must produce at least 400 almond-filled croissants due to customer demand. Bear claw profits are 20 cents each, and almond-filled croissant profits are 30 cents each. -What is the formulation for this problem?

The owner of Chips etc. produces two kinds of chips: lime (L) and vinegar (V). He has a limited amount of the three ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of lime chips are $0.40, and for a bag of vinegar chips $0.50. -What is the formulation for this problem?

A credit union wants to make investments in the following: Type of Investment Annual Rate of Return (\%) Vehicle loans 7 Consumer loans 9 Other secured loans 10 Signature loans 11 Risk-free securities 8 The firm will have $2,500,000 available for investment during the coming year. The following restrictions apply: ∙ Risk-free securities may not exceed 30% of the total funds, but must comprise at least 5% of the total. ∙ Signature loans may not exceed 12% of the funds invested in all loans (vehicle, consumer, other secured loans, and signature loans) ∙ Consumer loans plus other secured loans may not exceed the vehicle loans ∙ Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $2,500,000 be allocated to each alternative to maximize annual return? What is the annual return?