The ABC Company is planning its production for the next month. ABC has the capability to

manufacture three different products. Associated with product $j(j=1,2,3)$ are the following

quantities:

The amounts of each of three scarce resources consumed during the production of each

unit of product $j,$

The unit profit $p_j$ for product $j,$ and

A fixed charge $($cost$)k_j$ is incurred if and only if the production level of product $j$ is

positive.

Table $2$ summarizes these data as well as the availability of each of the three resources during the

next month.

TABLE $2$: Data for ABC's Fixed$-$Charge Problem

ABC estimates it can sell its entire production, regardless of its product mix. Subject to the

constraints on resource availabilities, ABC wishes to determine the optimal product mix $-$ that is$,$

the production levels for each of the three products that will maximize next month's total profit.