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

This game challenges you to correctly utilize a number of derivation rules:

  • 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

When setting the sale item for a category, you to first select the item you think will generate the greated revenue. Click on each item bring up that item's projected-revenue chart, and use that visualization to help you determine which item to profile on the web page. (Note: If you're not sure which item to select, you can calculate the optimal price for each item and then plug that into the projected revenue function to make a more accurate assessment)

Tip: Defining the optimal price

Once you select the item you think will generate the greated revenue, it's time to define its optimal price. To do so, follow these steps to calculate the local maximum for the projected-revenue function:

  1. Find the function you want to optimize
  2. Differentiate that function.
  3. Set the derivative equal to zero
  4. Solve for the quantity of interest.
Remember, if you price too high demand may wither, but if you price too low you'll leave money on the table!

Tip: Determining the optimal free-shipping time period

Finding the minimum point in a function also has practical business applications, especially when assessing costs estimates. Luckily, the approach to find the optimal cost structure is the same as the process utilized to set pricing:

  1. Find the function you want to optimize
  2. Differentiate that function.
  3. Set the derivative equal to zero
  4. Solve for the quantity of interest.
Keep in mind that shippings costs can quickly erase potential sale profits, so be precise!