Functions of several variables: extremes, Lagrangian problem The TV factory produces two models of TVs: luxury and standard. The plant manager has determined that the annual profit of the plant will be P (x; y) = -0.3x20.5xy-0.4y2 + 85x + 125y-2500 for the production of x hundreds of luxury and y hundred standard TVs per year. The factory can produce exactly 30,000 TVs. Determine how many luxury and how many standard TVs need to be produced to maximize factory profits. Evaluate the change in profit if the number of TVs available can be reduced by 100 units