A factory is producing DVD and Blu Ray discs. For each case of DVDs they make $180 profit. For each case of Blu Ray they make $250. The DVDs take 3 minutes of machine time and 7 minutes of labor. The Blu Rays take 4 minutes of machine time and 12 minutes of labor. The maximum machine time available is 210 minutes. The maximum labor available is 546 minutes. How many DVDs and Blu Rays should be made to maximize profits?
Let d = # dvd's
Let b = # blu-rays
You know:
3d + 4b <= 210
7d + 12b <= 546
p = 180d + 250b
graph those two lines and p is max at their intersection.
profit is max at p(42,21) = 12810