# nufacturing company produces the quantity q of a product that depends on W workers and a capital 3 1 amount K as given by the equation q = 6 (W); (K)?…

Question 5 8 marks A manufacturing company produces the quantity q of a product that depends on W workers and a capital 3 1amount K as given by the equation q = 6 (W); (K)?Labour costs are \$10 per worker and capital costs are \$20 per unit of capital and the total cost is \$3000. (8)lb)(C)(d) (E) Formulate the Lagrange function for this problem. (1 mark)Find the partial derivatives of the Lagrange function. {1 mark)Solve the system of equations to ﬁnd the optimal solution. {2 marks) Demonstrate the following economic principle for the optimal solution found in (c) that The marginal productivity of labour 3—3) :The marginal productivity of capital (2%)= Cost per unit of labour : Cost per unit of capital (2 marks) Recompute the optimal values for W and K when the total cost is increased by \$1 and check that thisallows for the production of an extra A units whereh is the Lagrangian multiplier. (2 marks)