4 The Deering companys production function is Q 20LK where

4) The Deering company\'s production function is Q = 20LK, where Q is the output rate, L is the number of units of labor used, and K is the number of units of capital. The price of labor is $4.00 per unit and the price of capital is $10.00 per unit. What combination of inputs should be used to produce 288 units of output?

Solution

Answer : Given , Q = 20LK, Q = 288

Let price is denoted by P. Now PL = $4 => L = 4/P ;

PK = $10 => K = 10/P.

Now putting all values in producin function we get,

288 = 20 * 4/P * 10/P = 800/P²

=> 288*P² = 800 => P² = 800/288

=> P² = 2.777 => P = 1.666

Now, L = 4/1.666 = 2.4 ; K = 10/1.666 = 6.002

Therefore, the combination of inputs (labour + capital) is (2.4 + 6.002) = $8.402