A firm uses two inputs to produce its output via Cobb$-$Douglas production function $Q=K^{}{L}^{}$ where $=0\mathrm{.}4$ and $=0\mathrm{.}6.$ Its currentlevel of inputs is $K=40,L=120.$ The firm will introduce a new technology that will change the $-$exponent on its production function to $=0\mathrm{.}605$ with no change to $.$ Use differential calculus to estimate the input combination which will keep the total output the same, and the sum of the inputs the same. What's your conclusion? $[$Hint: Work with the system $K^{}{L}^{}=c($or better $lnK+lnL=lnc)$ and $K+L=160](20$ points$)$Please use handwriting no ai answer please