Use DESMOS (desmos.com/calculator) to solve the problems and upload your solutions in the link provided.

Problem 1

Maximize P = x + 2y subject to

x + 2y < 4

2x + 3y > 12

x > 0, y > 0

Problem 2

Suppose that a web server company wants to buy new servers to replace outdated ones and has two options to choose from. There is a standard model which costs $400, uses 300W of power, takes up two shelves of a server rack, and can handle 1000 hits/min. There is also a cutting-edge model, which costs $1600, uses 500W of power, but takes up only one shelf, and can handle 2000 hits/min. With a budget of $36,800, 44 shelves of server space and 12,200W of power, how many units of each model should the company purchase in order to maximize the number of hits it can serve every minute?

Problem 3

The liquid portion of a diet is to provide at least 300 calories, 36 units of vitamin A, and 90 units of vitamin C daily. A cup of dietary drink X provides 60 calories, 12 units of vitamin A, and 10 units of vitamin C. A cup of dietary drink Y provides 60 calories, 6 units of vitamin A, and 30 units of vitamin C. Now, suppose that dietary drink X costs $.12 per cup and drink Y costs $.15 per cup. How many cups of each drink should be consumed each day to minimize the cost and still meet the stated daily requirements?