The Server Problem

General description A firm that assembles computers and computer equipment is about to start production of two new Web server models. Each type of model will require assembly time, inspection time, and storage space. The amounts of each of these resources that can be devoted to the production of the servers is limited$.$ The manager of the firm would like to determine the quantity of each model to produce in order to maximize the profit generated by sales of these servers.

Additional information In order to develop a suitable model of the problem, the manager has met with design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information:

The manager also has acquired information on the availability of company resources. These $($daily$)$ amounts are:

Resource

Assembly time

Inspection time

Storage space

Amount Available

$100$ hours

$22$ hours

$39$ cubic feet

The manager also met with the firm's marketing manager and learned that demand for the servers was such that whatever combination of these two models of servers is produced, all of the output can be sold.

$(1).|$

$(2)...$

$(3)?.,$

$()($basic feasible solution$)...$

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$(4)\backslash (\backslash$left$($C$\_\{1\},$ C$\_\{2\}\backslash$right$)\backslash )($range of optimality$).$

$(5)($right$-$hand side$)($range of feasibility$)...$

$(6)($shadow price$)?.,$