2) in the numerical example mentioned onn the slides on two part pricing with heterogeneouscustomers (see the ‘challenge’ in the second remark of one of the slides on two-part pricing), assumethata1= 4,a2= 6,c= 0,n1= 1,000 andn2= 500. solve for the optimal (t, p). (hint: thederivative of (n1+n2)×t(p) + (p−c)×(n1×(a1−p) +n2×(a2−p)) with respect top, wheret(p) = (a1−p)2/2, is given by−(n1+n2)×(a1−p) +n1×(a1−p) +n2×(a2−p)−(p−c)×(n1+n2). my suggestion is to first solve the example suggested on the slides as practice, and then do this problem.)3) consider a firm that sells to two groups of customers with demandsp1= 100−q1andp2= 50−q2. the firm’s marginal cost ismc(q) = 0.5q, whereq=q1+q2. find the optimalgroup pricing strategy. obtain the price elasticities of the two groups at the profit maximizingprice-quantity combinations. (hint: you need to solve two equations in two unknowns.)

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin. answer in one word. part bfind e(r), the magnitude of the electric field at distance r from the point charge q. express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q. express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r