Two firms 1 and 2 are using both capital (K) and labour (L) to produce identical products. They have different technologies in their productions, which are described as the following production functions:

f1(K1,L1) = aK1 +bL1; f2(K2,L2) = min{aK2,bL2},

where a,b are two positive constants and the subscripts 1 and 2 represent different firms, respectively. The market prices for capital and labour are r and w.

(a) What are the cost-minimizing values of K1 and L1 if Firm 1 produces a given number q1? Show your work and illustrate your answer using an appropriate diagram with necessary details. Note that both explanations and a diagram are required.