Suppose a firm is producing Thneeds (these are the things we need by the way). Thneeds are produced using the production function Q=20K^0.5L^0.4, where Q represents the number of Thneeds produced, L is the quantity of labour input, and K is the quantity of capital input.It is further known that the current wage rate is $25 and the current rental cost of capital is $50.

a) What is the optimal capital to labour ratio (to 3 decimal places)?

K = ...... L

b) Given the information above, what is the minimum cost of producing 2000 Thneeds?

c) In the long run, if the firm would like to minimize its total costs to $5000, how much labour (L*) and capital (K*) should the firm use?

d) How many units will be produced with a minimum cost of $5000 (round to the nearest whole number)?

Please show your calculations.