Lists Business#

Section Title: Lists Business

Business Applications#

Question-1: Max of Revenue#

Revenue (R) is the product of the number (n) of items sold and the price (p) of the item.

  • \(R = p\cdot n\)

The number of item sold is given by the following equation: \(n = -1.5p+30\)

  • Construct a list that consists of the revenues for \(0\le p \le 20\).

  • Plot the graph of revenue for \(0\le p \le 20\)

Question-2: Profit#

Profit (P) is the difference between Revenue and Cost

  • \(Profit = Revenue - Cost\)

The monthly fixed cost of a cable factory is 1500 dollars. Each cable costs 13 dollars and sells for 25 dollars.

  • For what number of cables produced profit is zero.

    • Hint: Calculate the profit for \(n\) between 1 and 400.

  • Construct three lists that consist of the revenues, costs, and profits for \(0\le p \le 400\).

  • Plot the reveue, cost, profit for producing up to 400 cables.

  • Draw a vertical line where the profit is zero for \(n\).

Sample Plot:

In this plot, there is a vertical line between x = 100 and x = 200, along with three dashed lines representing Revenue, Cost, and Profit. The Revenue line starts at the origin and has a positive slope. The Cost line begins above the origin on the y-axis and also has a positive slope. The Profit line starts below the origin on the y-axis and has a positive slope as well. The Revenue and Cost lines intersect at a point on the red vertical line.

Question-3: Break-Even Point#

Break-Even Point is the point where total cost equals total revenue, meaning profit is zero.

For the given cost and the revenue functions find the break-even point and plot it.

\(C(n) = 0.5n +2000\)

\(R(n) = 2.5n\)

Hint: Calculate the cost and revenue for n between 1 and 10,000.

Sample Plot:

In this plot, there is a vertical line between x = 100 and x = 200, along with three dashed lines representing Revenue, Cost, and Profit. The Revenue line starts at the origin and has a positive slope. The Cost line begins above the origin on the y-axis and also has a positive slope. The Profit line starts below the origin on the y-axis and has a positive slope as well.The Revenue and Cost lines intersect at a point on the red vertical line. The coordinates of this point are (1000, 2500), and it is referred to as the break-even point.

Question-4: Exponential Depreciation#

The value \(V\) of a truck in dollars is given by the formula \(V(t)=140000(1.35)^{-0.6t}\) where \(t\) is the age of the truck in years.

  • Plot the graph of values of the truck in 30 years.

Question-5: Demand#

If the demand function is given as the following linear relation \(p = -2q+300\).

  • Plot the demand function for \(1\le q\le 200\).

Question-6: Supply Function#

If the supply function is given by the linear relation \(p = 4q+100\).

  • Plot the supply function for \(1\le q\le 100\).

Question-7: Equilibrium Point#

An equilibrium point is where the demand and supply curves intersect.

For the given demand and the supply functions find the equilibrium point and plot it.

Demand: \(p(q) = -0.03q + 1000\)

Supply: \(p(q) = 0.02q + 400\)

  • Hint: Calculate the demand and supply for \(q\) between 0 and 20,000.

Sample plot:

In this plot, there are two dashed lines representing Demand and Supply. The Demand line begins above the origin on the y-axis and has a negative slope, while the Supply line also starts above the origin on the y-axis but has a positive slope.The Supply and Demand lines intersect at a point known as the equilibrium point. The coordinates of this point are (12000, 640).

Question-8: Stock Percentage Changes#

The following is a list of the prices for Tesla stock over a certain period of time.

stock_prices = [174.9499969482422,
 186.60000610351562,
 180.11000061035156,
 173.74000549316406,
 179.24000549316406,
 176.75,
 176.19000244140625,
 178.7899932861328,
 178.0800018310547,
 176.2899932861328,
 174.77000427246094,
 175.0,
 177.94000244140625,
 177.47999572753906,
 173.7899932861328,
 170.66000366210938,
 177.2899932861328,
 182.47000122070312,
 178.00999450683594,
 187.44000244140625,
 184.86000061035156]

Create a list of percentage changes using the stock_prices list.

  • The first element of the percentage list is np.nan because there is no price available for the previous day.

Question-9: Stock Behavior#

The following is a list of the prices for Tesla stock over a certain period of time.

stock_prices = [174.9499969482422,
 186.60000610351562,
 180.11000061035156,
 173.74000549316406,
 179.24000549316406,
 176.75,
 176.19000244140625,
 178.7899932861328,
 178.0800018310547,
 176.2899932861328,
 174.77000427246094,
 175.0,
 177.94000244140625,
 177.47999572753906,
 173.7899932861328,
 170.66000366210938,
 177.2899932861328,
 182.47000122070312,
 178.00999450683594,
 187.44000244140625,
 184.86000061035156]

Create a list indicating the behavior of stock prices as Increasing, Decreasing, or Flat using the stock_prices list.

  • Count how many days the stock price went up.

  • The first element of the behavior list is np.nan because there is no price available for the previous day.