A company is using linear programming to determine the optimal production mix for two

products, A and B$.$ The objective is to maximize profit. The original linear programming

problem is as follows:

Maximize $Z=3A+5B$

subject to:

$(1)2A+B10$;

$(2)A+3B12$;

$(3)A,B0.$

The company has found the optimal solution to be $A=3\mathrm{.}6,B=2\mathrm{.}8,$ and the maximum profit

$Z=24\mathrm{.}8.$

Now, the company is considering making changes to the problem. They anticipate the

following changes:

$($a$)$ The profit from product A may change from $$3$ to $$4..$