3 MATH 151 3. Bob builds sheds. To build a small shed he needs 20 sheets of dry wall and 30 studs. To build a large shed he needs 30 sheets of dry wall and 90 studs. He has 120 sheets of dry wall and 270 studs available. If Bob makes $390 profit on a small shed and $520 on a large shed, how many of each type of shed should Bob build to maximize his profit? (a) Let x be the number of small sheds and y be the number of large sheds. List [2 marks] all constraints, including the hidden constraints (4 total). (b) Roughly sketch and shade the feasible region. [3 marks] (c) Give an expression for total profit. [2 marks] (d) Find the vertices of the feasible region (4) and use the vertex method to find [3 marks] out how many large sheds and how many small sheds Bob should build.