An airline has a new airplane that will be fitted out for a combination of first and second class passengers.

An airline has a new airplane that will be fitted out for a combination of first and second class passengers. A first class seat will cost $120 on a certain one-way trip and a second class seat $80. The seating capacity of the plane is 200 second class seats. A first class seat takes 1.2 times the floor area of a second-class seat. It is assumed that a first class passenger and his luggage weigh 250 lbs, while a second-class passenger and his luggage weigh 210 lbs. If the weigh limit on the plane is 45,000 lbs, how many seats of each type should be offered it is assumed that all seats in both classes will be sold?

Showing a matrix is totally unimodular

This problem was a sample exam question taken from a text book. This problem is about showing a matrix is TU. This problem can be found in the Wolsey text book called "Integer Programming". A useful resource is "Integer and Combinatorial optimization" by Wolsey and Nemhauser.

Old Tennessee Distillers, Inc., is a large distiller in rural Tennessee with a strong brand recognition for three major brands of blended whiskey.

Old Tennessee Distillers, Inc., is a large distiller in rural Tennessee with a strong brand recognition for three major brands of blended whiskey. Old Tennessee blends five bourbons into the three final branded blends of whiskey. Brand A is a blend of 20% component bourbon 1, 15% component 2, 30% component 3, 10% component 4, and 25% component 5. Similarly, Brand B is produced from 10%, 40%, 20%, 10%, and 20% of the same ordered component bourbons. For Brand C, the bourbon component percentages are 30%, 10%, 10%, 20%, and 30% respectively. There are 50,000 gallons of bourbon component 1 available each week at a cost of $2.50 per gallon. Similarly, availabilities of the remaining bourbo... click for more

The Midland Tool Company manufactures prefabricated metal housings and covers for consumer products

The Midland Tool Company manufactures prefabricated metal housings and covers for consumer products under contracts from finished goods producers on four heavy presses of different sizes and different requirements. Currently, the company has a contract to manufacture three products that each require operations on any one of the four presses. The contract requires 400 units of product 1; 570 units of product 2; and 320 units of product 3. The time required, in minutes, for each product on each press follows. Machine Product 1 2 3 4 1 35 41 34 39 2 40 36 32 43 3 38 37 33 40 Machine 1 is available for 150 hours during the contract period, machine 2 is similarly available for 240 hour... click for more

Linear programming

Fairview Manufacturing Company is considering a number of expansion projects to take place over the next four years. Specifically, Fairview Manufacturing needs to utilize a capital budgeting process to select appropriate opportunities from a total of five approved projects under consideration. Each project requires lump sum capital outlays over one or more of the years in the budgeting period where each year is subject to a budgetary (capital) constraint. The objective is to select the set of projects that maximizes a measure of total return on investment (net present value) without violating the capital requirements in each year. Project 1 requires a capital outlay of $300,000 in year 1... click for more