Royal Motors Ghana Limited is a sole producer of tricycles in Ghana. It has set up two production facilities: the Eastern Facility and the Southern Facility. For this firm, Q$,$ units are produced in the eastern facility and $2$ units are produced in the southern facility, so that Q$=$Q$1+$Q$2.$ The demand function for the firm is given as Q$=1040-0\mathrm{.}2$P$.$ The total cost ofproducing the tricycles at the eastern facility is given by C$1($Q$1)=100+25$Q$1^2$; and that of thesouthern facility is C$2($Q$2)=120+50$Q$2^2.$

$$I.Determine the profit maximising level of the tricycles that the firm should produce at the two facilities.

ii$.$ Find the optimal price and the firm's profit.