Need help answering question 5! I've answered all the previous parts.

A. [This problem is based on Homework 1, Problem C and Homework 5, Problems A, G, H, and I.] A company has three production facilities that use input to produce output according to the pro- duction functions q = f1(21) = 6Vx1, q = f2(22) = 8V/x2, and q = f3( d & 4 - 2 = 0 = > * = jazz 16 = 21 27 2 2 - 16 21 9 11 11 daz = VII a3 - 2 = 0 = > h = 17123 d x da = 0 = 7 121 9 11 21 3 = a =7 23 = 9 al taztaz = X = > m, + 16241 + 121 _ X =7 36 241 = X 9 9 -7 2 1 = X 4 =7 02 = 41 = 7 23 = 1X 9 f (21 ) = 6 5x /4 = 3VX f2 (212 ) = 8 5 4x19 = 36 16 JX 3 f3 ( 213 ) = 2 / 11 ( 11X /36 ) 2 2 2 JX = II J X F (X ) = 35X+ 16 JX + 11 JX 6 3 3 3 = 125X2. Check directly that the marginal product of input is equal to the Lagrange multiplier. From Part 1 day = 2 = 2 do 4 doz do 11 = = 3. Assuming that the firm is competitive, buys input X at price w and sells output, q, at price p, find the firm's supply function, q(p, w). F (X ) = 125X TT = PF ( X ) - W X = 125X p - w X d x = 12P - W = 0 2 5X = > W = JX 6 P 6 P = 7 w = JX 8 ( P, W ) = 125X - 72p w4. Using the Lagrangean method, find the firm's cost function, C(q, w). F ( X ) = 125X Cost = wx F ( X ) = 9 = > 125X = = 7 VX = = 7 X = 144 ( ( 8 , W ) = W X = wa2 144 5. Show that the multiplier you found in the cost function calcu- lations is equal to some price in this problem, and explain why this is true