A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1a units turn out to be defective, where 1>1a>0. That is, only a fraction a of purchased units of input 1 actually contributes to producing output y. Letx1 and x2 be the quantities that are not defective and can be employed towards production.

1.Suppose the firm's production function is such that x1and x2 are perfect substitutes: each unit of output can be made with either one unit of x1 or 1/4 units of x2. Suppose w1=1 and w2=8. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if a_______.

2.Suppose the firm's production function is such that x1 and x2 are perfect complements: the firm needs 1 unit of x1 and 5 units of x2 to make each unit of output. Find the total cost of producing 5 units of output when w1=w2=1 and a=0.3.