How many cases of each will maximize the trucker's sales?

Question

A trucker carries cases of Big Red and Dr. Pepper into a region. His truck can carry 1000 cases total. He must carry at least 200 cases of Big Red and at most 400 cases of Dr. Pepper. Each case of Big Red is charged a $5 "import fee" and each case of Dr. Pepper is charged $10. The driver has abide the of $6000 to spend on import fees. If a case of Big Red sells for $20 and a case of Dr. Pepper sells for $25, how many cases of each should the driver carry in order to maximize his sales?

Answer 1

Let x = number of cases of Big Red and y = number of cases of Dr. Pepper. From the problem we know, x + y < 1000, x>200, y<400, 5x+10y < 6000. Graph these and find the points of intersection. Use those points to plug into 20x + 25y to see which ordered pair maximizes the sales.