Talbot Industries manufactures two models of wireless headset: TI$-12$ and TI$-28.$ Each product requires time on a single

machine. The machine has a monthly capacity of $672$ hours. Total market demand for the two products is limited to $2,320$

units of $TI-12$ and $1,160$ units of TI$-28$ monthly. Talbot is currently producing and selling $1,660$ TI$-12$ models and $812TI-28$

models each month. Cost and machine$-$usage data for the two products are shown in the following spreadsheet, which

analysts at Talbot use for production planning purposes:

Required:

a$.$ What is the optimal production schedule for Talbot Industries? In other words, how many TI$-12$s and TI$-28$s should the

company produce each month to maximize monthly profit?

b$.$ If Talbot Industries produces at the level found in requirement $($a$),$ how much will monthly profit increase over the current

production schedule?