Can you please check my answers for accuracy?

Question:

What are the cost-minimizing values of L and K for the following functions? Note that w = r = 2 and the production target is 50.

(a) (5) q = f(L, K) = 2LK

(b) (5) q = f(L, K) = 2L + K

(c) (5) q = f(L, K) = min{2L, K}

(d) (5) q = f(L, K) = 2L + ? K

q = f ( 1 , k ) = 2 LK At : optimal : dit/draws 2 K Z w [ K = L ]. substituting in production function q = 2 LK (: 9=5 0 ] 50= 2 ( 1) ( L ) 2 5 = 12 =7 1= 5] so; [ Lack " = 5 ] cost minimizing inputs q z f / L , v ) = 2 2 + K Slope tol goughants = - af/ dL .= 2 = slope of gsocosts - - Z slope of gooquants (7 ( slope of iscosts ] Isoquant is steeper . Do only Labor is used [: 9= 50] 50 = 2L [ 25 = L ] so ; [L = 25 ; Kzo ] inputs