a) The equilibrium point is when supply and demand balance, so 1.5p^2-30p+50=0.25p^2-50. So 1.25p^2-30p+100=0. Multiply through by 4: 5p^2-120p+400=p^2-24p+80=0=(p-4)(p-20)=0. So p=4 or 20, both of which are less than RM50. I suspect that RM20 is the correct price, even though the domain given contains an error.
b)
i) Cost, c=84+1.60N; selling price, s=2.20N, where N is the number of items made and sold. Profit, p=s-c=2.20N-84-1.60N=0.60N-84.
ii) Break-even quantity is N where c=s or p=0: 0.60N=84, N=84/0.60=140.
iii) p=2.40N-84-1.60N=0.80N-84, so when p=0 N=84/0.80=105. The break-even quantity has reduced by 35 from 140 to 105.
c)
i) Revenue, r, from sales=pq. Substitute p=2320-8q: r=q(2320-8q)=2320q-8q^2=8(290q-q^2)=-8(q^2-290q+145^2)+8*145^2=-8(q-145)^2+8*145^2, (ii) which has a maximum value when q=145, because the first term becomes zero, iii) maximum r=RM168200 when q=145 (and p=RM1160).