Welcome to the Student Guide for OPTIMIZATION!

### Overview

Optimization puts you in the driver seat as the online sales manager for a top e-commerce company. It's cyber-week, the highest revenue generating week of the year and you'll use your knowledge of derivatives to optimize prices, minimize costs and ultimately maximize profit.

Your instructor will determine the easiest way for you to access the game. To make sure you find your way, we've created a walkthrough tailored to the access path your instructor selected:

### Gameplay

### Using Optimization

Optimization is a process to identify maximum or minimum points in real function. In this game, you are asked to select the highest grossing product, set the optimal price, and offer the most cost-effective free-shipping period. Run the most profitable e-commerce site in your section by utilizing what you know about optimization to inform your decisions. Good luck!

### Tip: Concepts to keep top of mind

**Power Rule**: Remeber to bring down the power, then knock the power down 1. Adjacent concepts to keep in mind the derivative of a straight line must be its slope and the derivative of a constant is zero.**Product Rule**: Sometimes processes need to be described by more complicated expressions. The first expression is the product rule for derivatives which states that if a derrivative exists for two functions f(x) and g(x) then the product is differentiable. Written out, (f*g)' = f'*g + f*g'.**Chain Rule**: The second expression covered in this game occurs when the result of one process is the input for another. For example, you have a function g(t), and another, f(x) where x = g(t). Here the rule states that the composition of the functions, f and g, is written as f (g(t)) and (f (g(t))' = f′(g(t)) × g′(t).

### Tip: Choosing which item to promote

### Tip: Defining the optimal price

**Find the function**you want to optimize**Differentiate**that function.- Set the derivative
**equal to zero** **Solve for the quantity**of interest.

### Tip: Determining the optimal free-shipping time period

**Find the function**you want to optimize**Differentiate**that function.- Set the derivative
**equal to zero** **Solve for the quantity**of interest.

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