Suppose a consumer buys clothing for the heat it provides and that each unit of clothing provides 2 units of heat. assume that the consumer also buys housing for the shelter it provides, and that one unit of housing provides one unit of shelter. if h is the number of housing units and c is the number of clothing units consumed, then his utility is u(h, c)min h, 2c. the per-unit prices of housing and clothing are ph and pe, respectively, and his income is m.

(a) set up the maximization problem and derive the demand functions for h and c*.
(b) re-do part (a) assuming that u h. c) h 2c, ph-2. pc-3. and m-300.