Select the Get help button to view a step-by-step solution guide.A company sells a set of nonstick pans and stainless steel pans. The profit from the sale of these pan sets is given byP(n,s)=90n+167s-0.1ns-0.2n2-0.4s2-11600 dollars where n dollars is the price of the nonstick pan set and s dollars is the price of the stainless steel pan set.Calculator Checkpoint: P(40,60)=20a. Write out the system of equations that can be used to find the critical point ofP(n,s). Enter your answers as a list, separated by a comma.Note that your equations may be rearranged into any equivalent form and still be accepted if correct.b. Find the critical point ofP(n,s).(Round your answers to the nearest cent.)The critical point occurs when the price of the nonstick pan set is $and the price of the stainless steel pan set is $, which gives a profit of $c. Find the second partial derivatives matrix at the critical point ofP(n,s).(Do NOT round your values.)d. Compute the determinant of the partial derivatives matrix found in Part c.(Do not round your answer.)Determinant =e. Classify the critical point found in Part b.The critical point found in Part bis