A van conversion company has fixed capital and labor expenses of $1.2 million per year, and variable expenses averaging $2,000 per van conversion. Recent experience suggests the following annual demand for their products:
Q = 1000 - .1P
Where Q is the number of van conversions (output) and P is price.
Calculate the profit-maximizing output, price, and profits.
Assuming a parts shortage limits their output to 300 conversions per year, use the Lagrangian multiplier method to calculate the profit-maximizing output, price, and profits.
Calculate and interpret the Lagrangian multiplier.