7. The production function of a certain good Q that is produced with inputs q1,q2 and q3 (quantities) is: Q(q1, q2, q3) = 150 - (q1 - 3)2 - (q2 - 8)2 - (q3 - 5)2. We wish to determine the combination of inputs that maximizes the production of good Q a) Find the critical point (q∗1, q∗2, q∗3) of Q, from the first order conditions. b) Show, through the Hessian matrix criterion, that the obtained critical point corresponds to a maximum of Q. c) Calculate Q∗. Please explain step by step and be specific.

7. The production function of a certain good Q that is produced with inputs q₁,q₂ and q₃ (quantities) is:
Q(q₁, q₂, q₃) = 150 - (q₁ - 3)² - (q₂ - 8)² - (q₃ - 5)².
We wish to determine the combination of inputs that maximizes the production of good Q
a) Find the critical point (q∗1, q∗2, q∗3) of Q, from the first order conditions.
b) Show, through the Hessian matrix criterion, that the obtained critical point corresponds to a maximum of Q.
c) Calculate Q∗. Please explain step by step and be specific.