$Q=120x-5x^2+80Y-3Y^2-4xY$

$Q=$ total chair frames produced per day

$x=$ worker$-$hours per day

$Y=$ machine$-$hours per day

The firm currently uses $8$ worker$-$hours per day $)=(8$ and $6$ machine$-$hours per day $)=(6.$ Assume that each chair frame is sold to furniture assemblers for $$3,$ wage rates are $$25\mathrm{.}50$ per hour, and machine time is leased for $$48$ per hour.

a$.(7$ pt$)$ Calculate $M{P}_x$ and $M{P}_y$ at the current input usage levels $)=8,Y=(6.$

b$.(4$ pt$)$ Is the firm currently operating with a least cost combination of inputs? If not, which input is more cost efficient?