Erika Entrepreneur assembles laptop computer systems in her home to finance her graduate education. She makes and sells two types of units, both using the same frame. The deluxe model has 1024 megabytes of RAM memory, a 16 gigabyte hard drive, and a communication card; it sells for

$1400 per unit. The cheaper basic model, which sells for $1000, has only 512 megabytes of RAM memory, a 4 gigabyte hard drive, and no communication card. RAM in both models is built up by installing the requisite number of 256 megabyte chips.

Component Frames 256 MB Chips 16 GB Drives 4 GB Drives Comm Cards On Hand 18 72 7 11 3 Min Purchase 5 48 10 8 3 Max Purchase 40 182 30 64 25 Price/Unit $700 $75 $300 $110 $250 The table shows the number on hand at the beginning of the current month for each of the components Erika uses, along with the minimum and maximum she can buy if she makes a new purchase, and the unit price that would apply.

Note that her suppliers do not allow Erika to buy fewer than the minimum nor more than the maximum shown, and only one purchase per month is allowed. Within these limits Erika wants to decide a production and procurement plan that will maximize her gross profit (sales - cost) for the coming month.

(a) Although the numbers of components used and purchased must obviously be integer, explain why it would be good OR modeling to represent them as nonnegative continuous decision variables. Also indicate what issues are left that make the problem discrete.

(b) Formulate Erika’s problem as a Mixed-

Integer Linear Program. Be sure to define all your decision variables and annotate objectives and constraints to show their meaning.