A firm is considering bidding for the franchise to sell lemonade and corndogs at the Illinois State Fair. It estimates…

A firm is considering bidding for the franchise to sell lemonade and corndogs at the Illinois State Fair. It estimates the demand functions for lemonade and corndogs respectively as:
D_L=20-4p_L- p_c
D_C=15-p_L-p_C
where D_L is demand for lemonade in thousands (of cups) per fair, D_C is demand for corndogs in thousands per fair, pL is the price of lemonade per cup, and pc is the price of a corndog. The unit cost of supplying a corndog is constant at $0.1, and the unit cost of a cup of lemonade is likewise constant at $0.5. Assume the Fair looks after all the other costs (i.e., assume there are no other costs to this firm).
Find the upper limit to the amount the firm would bid for the franchise (per year).
Check to make sure your second-order condition is satisfied.
Extra Credit: Interpret the demand functions (especially the cross effects)