can you help me with this question? thanks

. Recall that if the supply of a commodity is represented by S and the demand of the same quantity by D, then the quantity of a commodity available at a particular time is given by q' (t) = S D. In the lecture notes we used this to generate a differential equation for price, p(t), by assuming that p' ~ q'. In general, 13' can depend on q in much more complicated ways. Assume that the price of a particular commodity changes according to: dp a = (D S) where (a:) = m x+225 Suppose the price and demand of the commodity we are selling are governed by the equations S(p) = 50 20p + 5p2 and D(p) = 50 + 1001) 41,2. (a) Find the equilibria points for the differential equation. (b) Find the general solution to the differential equation. (Note: you will not be able to errplicz'tly solve for p(t)). (0) Sketch a plot (either by hand or with software) with p' (t) on the vertical axis and p(t) on the horizontal axis for p E [0, 20]. ((1) Suppose 19(0) = pg 2 0. Using your plot from part (c), determine lim p(t) for each value of t>oo p0. Note that at p0 = 15, p' (t) is not dened. Does this contradict the E/ U theorem