Suppose a firm can produce the same product using any combination of three plants with cost functions c1(q1)=q12,c2(q2)=2q22,andc3(q3)=3q32 where qj refers to the outputs produced in plant j=1,2,3. (a) If the firm wants to produce a level of output Q, what fraction of this output should be produced in plant 1 and how much in plant 2? Denote these amounts as q1(Q) and q2(Q) (b) What is the joint total cost (JTC) of producing any output level Q ? (There is no need to simplify.) Suppose a firm can produce the same product using any combination of three plants with cost functions c1(q1)=q12,c2(q2)=2q22,andc3(q3)=3q32 where qj refers to the outputs produced in plant j=1,2,3. (a) If the firm wants to produce a level of output Q, what fraction of this output should be produced in plant 1 and how much in plant 2? Denote these amounts as q1(Q) and q2(Q) (b) What is the joint total cost (JTC) of producing any output level Q ? (There is no need to simplify.)