Amos Jones and Andrew Brown own and operate Amos & Andy, Inc., a Minneapolis-based installer of conversion packages for vans manufactured by the major auto companies. Amos & Andy has fixed capital and labor expenses of $1.2 million per year, and variable materials expenses average $2,000 per van conversion. Recent operating experience suggests the following annual demand relation for Amos & Andy products:

Q = 1,000 - 0.1P

where Q is the number of van conversions (output) and P is price.

A. Calculate Amos & Andy's profit-maximizing output, price, and profit levels.

B. Using the Lagrangian multiplier method, calculate profit-maximizing output, price, and profit levels in light of a parts shortage that limits Amos & Andy's output to 300 conversions during the coming year.

C. Calculate and interpret λ, the Lagrangian multiplier.

D. Calculate the value to Amos & Andy of having the parts shortage eliminated.