Q$2.$

A finserv company is serving four clients A$,$ B$,$ C and D$.$ The company will not entertain more than $100$ calls per day. The company has an upper limit of $50$ calls per day for client A$,45$ calls per day for client B$,40$ calls per day for client C and $35$ calls per day for client D$.$ The clients uses an automated hotline for the finserv company to book service calls whose maximum daily availability is $400$ minutes. The hotline time required to book a call by the clients are fixed at $3$ minutes per call per client. The commission for each booked call by the clients are at $$20$ for A$,$ $$35$ for B$,$ $$30$ for C$,$ $$50$ for D$.$

Determine an optimal call scenario for the finserv company.

Find the dual price of overall calls.

Determine the dual price of Bs call and its allowable range. If Bs call limit is raised by $5$ calls, what will be the new solution and new revenue.

Check whether it is allowable to change the hotline time availability by $10\%.$ If allowable, use the dual price to determine the effect of this change on the solution.

$($You are allowed to use software for solving this problem$)$