Question 1 A company produces two goods, A, and B. The number of items of each are g, and gg, respectively. The company's objective is to produce 300 units while minimizing its production costs, TC. The firm's associated joint total cost function is given by TC(qa q98) = 2q; + q5 + qaqp + 120q, + 100 (a) Determine the equation of the constraint based on the firm's objective. (b) Use the Lagrange multipliers method to determine the number of goods of each type needed to minimise the cost. We assume that the second-order conditions of the minimisation problem are satisfied. (c) Find the minimum cost subject to the given constraint. (d) Use the value of the Lagrange multiplier, A, to estimate the new optimal (minimum) total cost if the production level rises by 1 unit