Q3. Suppose a firm producing widgets on two assembly lines operates with the following

Total Cost function:

                                    TC = 7x² + 10y² – xy

where x represents the number of widgets produced on one assembly line and y the

production on the second. The firm is under contract to produce 48 widgets.

   (a) Use the Lagrangian method to calculate the least-cost allocation of production to the

two assembly lines.

(b) At what price must this firm sell its widgets in order to break even?

(c) Suppose a customer offers this firm $350 for one of its widgets but to make this

widget the firm has to stretch its total output to 49 widgets. Should the firm accept or

reject the offer and why?

(d) What would the firm’s total cost be equal to if it had to produce 47 widgets instead?