Given the following linear programming problem, maximize the solution and then explain how you arrived at your answer. Include the following: o Graph o Corner points o Checked solution A concession stand makes $1 on each hot dog and $1.50 on each hamburger. On a typical Saturday, the stand sells between 20 and 40 hot dogs and between 30 and 50 hamburgers. The total sales have never exceeded 80 items (hot dogs + hamburgers). How many hot dogs and how many hamburgers should be prepared to maximize profit? Variables x = Number of hot dogs y = Number of hamburgers Constraints 20 < x < 40 30 < y < 50 x + y < 80 Function to Maximize Profit P = 1x + 1.5y Graph the constraints on the same grid. You do not need to include your graph in your post. There will be two vertical lines (at x = 20 and at x = 40), there will be two horizontal lines (at y = 30 and y = 50), and a diagonal line (with a y-intercept at 80 and an x-intercept at 80). The overlapping shaded regions will form a square with the corner missing with 5 corner points (vertices). Four of the corner points are (20, 30), (40, 30), (40, 40) and (20, 50). What is the last corner point where the lines x + y = 80 and y = 50 intersect? Plug all corner points into the objective function to maximize profit. What is your largest profit? How many hot dogs and how many hamburgers should be prepared to maximize profit