I was tasked with this question, I am required to form a simple real life optimization problem with 3 variables with a constaint function using lagrege and d-test seperately. I am also stuck at the D-test part because as far as I know D-test only works on 2 variables. Can someone teach me how to form a problem with d test and lagrege solution seperately. Solution is seperate but based on the same question

Question 4 (10 marks) Discuss and solve ONE real-life optimization problem in which a function of THREE variables f (x, y, z) is maximised and/or minimised subject to ONE constraint of the form g (x, y, z ) =k . Your solution(s) should include the following: . A clear description of the proposed problem. . Formulation of the objective function and the constraint equation. . Detailed steps in solving the proposed problem by using both D-test method AND Lagrange multipliers method. . Conclusion