Suppose that Hump Ridge Company produces and sells two products, x and z, and that its total cost is given by

C = 4x² + 8z² - 2xz

Where x is its output per hour of the first product and z is its output per hour of the second product. The company has contracted with manufacturers to produce a total of 40 units each hour, but any mix of x and z is acceptable.

a) If the company wants to minimize its costs (without violating its commitments), how many x and z should it produce per hour?

b) What does λ equal? What does it mean?

c) If Hump Ridge Company is offered by a buyer $119.50 for one of its products but to make the product, Hump Ridge would have to stretch its total output  to 41 units per hour, should Hump Ridge accept the offer or not? Explain.