Given $($the same as in Homework $4)$ Cobb$-$Douglas production function $y=x_1^{0\mathrm{.}25}{x}_2^{0\mathrm{.}25},$ and input prices $r_1=4,r_2=1,$ derive the cost function. Show your solving steps and results in the "Homework $5$ File Submission". $(4$ points, which will be graded manually$)$

Question $1$

$4$ pts

Use the cost function you derived in Question $1,$ when output price is $p=10,$ solve for the profit maximization from output perspective. Your solution is $y^{**}=.$ The maximum profit is $-($Keep up to two decimal places for the calculation results.$)($Tip: You might want to compare with results of Question $3$ before you fill out the result.$)$