This open-book midterm exam must be completed individually. During the exam, you may use (graphical) calculators, tables, and the course formula sheet. Answers must include intermediate steps and explanations. 1. (a) (3 points) Determine the cost function C(q) for the marginal cost function MC(q) = 4q2 + 8q, given that the costs are 150 when 3 units are produced (i.e., C(3) = 150).(b) (3 points) Determine the integral function f vzt + 2dz. 2. (a) (3 points) How is the transpose of a matrix formed? Create a symmetric (3x3) matrix A, with a,, = 4. Demonstrate that the matrix you create is symmetric.(b) (4 points) Determine all solutions for the matrix equation Ax = b using Gaussian elimination, where -1 -2 0 0 A=1 2 4 2 and b= | 4 -3 2 -1 2 (c) (5 points) Given a company's revenue function R(qs, g) and cost function C(qy, q.) R(qi,q2) = (@1 @) (_24 _23) (g;) + (@) (388) , Cla @) = (@1 @) (_11 _11) (3;) + (0 @) Gg) +2 3. (a) (8 points) Draw the feasible region for the following LP model: max z = 2x1 + dxo subject to: 3r1 + 4z > 12, T 229