# Consider the following linear programming problem, where we are maximizing the profit

Subject: Business / Management
Question
Consider the following linear programming problem, where we are maximizing the profit (in KWD) obtained from selling standard (S) and
deluxe (D) laptop cases.
MAX 10*S+45*D s.t.
0.7*S + D &lt;= 630 (1) 0.5*S + (5/6)*D &lt;= 600 (2) S + (2/3)*D &lt;= 708
(3) 0.1*S + 0.25*D &lt;= 135 (4)
where,S and D refer to the number of standard and deluxe cases,
respectively.
Case Questions Prepare a report that answers the following questions:

1. In case your solution recommend not to produce one of the cases (S or D), advise on what should be changed so that particular laptop case is produced again.

2. Following the original model (part a), if the profit of each Standard case was increased to 12 KWD and the one for Deluxe decreased to 35 KWD, will the optimal solution change? What about the Profit? Explain. The optimal solution changes, because for standard case objective function can only increase by 8 units and deluxe case can only decrease by 20. Therefore, there will be a new optimal solution and there will be a new profit.

3. Following the original model (part a), assume that constraint (4) refers to the fabric capacity (in lb) that cannot be exceeded. If a supplier proposed to sell us 100 lb for a total price of 4000 KWD, should we accept his offer or no? Explain in detail w/o resolving your model.