3and 4 The AirAtlantic company wants to build a new factory

The AirAtlantic company wants to build a new factory, either in Halifax or in Truro(or both) and needs to decide whether to build a new warehouse (at most one) which must be built closed the city of a new factory. The company available $10 million dollars on hand to spend. The price and net present value (NPV) of each choice is listed below: The company wants to maximize the net present value. Formulate the problem as an integer programming problem. Suppose a new company make tablets and cell phones. The company can sell the tablet at a profit of $ 150 per tablet, and a cell phone at a profit of $80 per cell phone. Three chips are required for each tablet and two chips for each cell phone. The cell phone requires two cameras while the tablet requires just one. There are 5,000 chips and 3,000 cameras available. If any tablets are made, a set up cost of $2.000 is incurred, while if any cell phones are made, a set up cost of $1.500 is incurred. Finally, demand for tables is at most 2, 500. Formulate an IP to maximize profit.

Solution

Let x = number of tablets to be produced

And y= number of cell phones are to be produced

Profit

chips

cameras

150x – U (x 1)*2000

Tablets (x)

3x

1x

80y – U (y 1)*1500

Cell phones (y)

2y

2y

Total

5000

3000

Here in the table, U(x - 1) is unit step function which is equal to ‘1’ if x 1 otherwise it is zero. (This means if any tablet is manufactured then x 1 and thus U(x-1)*2000 corresponds to deduction of set up cost from the total profit). Similarly U(y - 1) takes care of deducting set up cost, if any cell phone is produced.

We have to maximize the profit. So, our objective function is

                                               Z = 150x + 80y – U (x 1) *2000 U(y-1)

We have maximum 5000 chips. So, 3x + 2y 5000

Similarly, for the cameras, we have x + 2y 3000

Finally, we have a limitation on the demand for tablets. So, x 2500

And the non-negativity constraints are x 0 and y 0. And x, y are integers.

Profit		chips	cameras
150x – U (x 1)*2000	Tablets (x)	3x	1x
80y – U (y 1)*1500	Cell phones (y)	2y	2y
	Total	5000	3000