Pens Inc have 2 machines which can each produce 10 pens per hour. Production runs for 6 hours per day, 5 days a week. Pens are kept in storage until they are sold on the website. The storage can hold a maximum of 2000 pens. Pens Inc begins manufacturing pens for the very first time at the start of week 1, and the storage is empty. Pens Inc sells their pens on their website. The pens retail for £10/unit and cost a total of £6/unit to manufactureThe only traffic to the site comes via Cost per Click (CPC) traffic - there is no organic traffic. The conversion rate on that traffic is 20%  Question 1Pens Inc have launched their first product, which sells 100 units in the first week, 120 in the 2nd week and 144 in the 3rd week. If sales continue to grow at this rate, how many pens will they have sold in total 8 weeks after launch?Question 2 *The storage is to be emptied every 8 weeks. What is the minimum number of pens that need to be sold per week to be sure that the storage doesn’t exceed maximum capacity by the end of week 8?Question 3 *What is the maximum CPC they should be willing to pay to ensure they breakeven?

Question 1:

The sales growth rate is 20% per week. To find the total sales after 8 weeks, we need to use the formula for the sum of a geometric series.

The first term (a) is 100, the common ratio (r) is 1.2 (representing the 20% growth), and the number of terms (n) is 8.

The sum (S) of the first n terms of a geometric series can be calculated using the formula:

S = a * (1 - r^n) / (1 - r)

Substituting the given values into the formula, we get:

S = 100 * (1 - 1.2^8) / (1 - 1.2)

S = 100 * (-21.99) / -0.2

S = 10995 units

So, Pens Inc will have sold 10995 pens in total 8 weeks after launch.

Question 2:

The two machines can produce 10 pens per hour each, for 6 hours a day, 5 days a week. So, in a week, they can produce:

2 machines * 10 pens/hour * 6 hours/day * 5 days/week = 600 pens/week

Over 8 weeks, they can produce:

600 pens/week * 8 weeks = 4800 pens

The storage can hold a maximum of 2000 pens. So, to ensure that the storage doesn’t exceed maximum capacity by the end of week 8, at least:

4800 pens - 2000 pens = 2800 pens

need to be sold. Dividing this by 8 weeks, we get:

2800 pens / 8 weeks = 350 pens/week

So, a minimum of 350 pens need to be sold per week.

Question 3:

The pens retail for £10/unit and cost £6/unit to manufacture, so the profit per pen is:

£10/unit - £6/unit = £4/unit

The conversion rate is 20%, so for every 5 clicks, one pen is sold. Therefore, to break even, the maximum Cost per Click (CPC) they should be willing to pay is:

£4/unit / 5 clicks = £0.8/click