Tangent Curves to Linear Functions (Wages and Cobb Douglas)

using Gnuplot, Gaston, Convex, SCS

L= 0:600

contour(K, L, (K,L)->.1*K^.5*L^1.5, xlabel="Leisure", ylabel="Consumption",labels=false)
#same function as a contour graph for somereason, doesn't reach

#now I need to add wages
problem = minimize(sumsquares(A * x - y), [x >= 0])
# looks about right, except if I want W*h-y, then I need to change variables
# "                                "  W*168-y, then I have a constant as x

Can I use the above to find where each wage rate (K=168-L* K/L) is tangent to a Utility curve?