Knights Wheels produces and sells bicycles and unicycles. Each bicycle requires $10$ hours of machine assembly and $6$ hours of manual assembly. Unicycles require $5$ hours of machine assembly and $8$ hours of manual assembly. Machine time is capped at $60$ hours while manual assembly time is capped at $48$ hours. Bicycle profit is $$200$ per unit, while unicycle profit is $$220$ per unit.

$1.$ What is the objective function?

$2.$ What is the complete set of constraints?

$3.$ All of the following are corner points in the feasible region except:

a$.(0,0)$

b$.(0,6)$

c$.(4\mathrm{.}8,2\mathrm{.}4)$

d$.(8,0)$

$4.$ What is the maximum profit that results from the optimal solution?