A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 11a units turn out to be defective, where 1>1>01>1a>0. That is, only a fraction a of purchased units of input 1 actually contributes to producing output y. Let 1x1 and 2x2 be the quantities that are not defective and can be employed towards production.

If rounding is needed, please round your answers to 3dp.

Suppose the firm's production function is such that 1x1 and 2x2 are perfect substitutes: each unit of output can be made with either one unit of 1x1 or 1414 units of 2x2. Suppose 1=1w1=1 and 2=7w2=7. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a_______.

Answer for part 1

uppose the firm's production function is such that 1x1 and 2x2 are perfect complements: the firm needs 1 unit of 1x1 and 44 units of 2x2 to make each unit of output. Find the total cost of producing 3 units of output when 1=2=1w1=w2=1 and =0.6a=0.6.

Answer for part 2