A stationery retailer generally prices portable computers using a 30 percent markup. The retailer expects to sell 100 portable computers at the 30 percent markup. How many units would it have to sell at a 10 percent increase in price from the original price to maintain the same gross profit?
To find the solution to this question, we need to first determine the original price of a portable computer before the 30 percent markup. Then we can calculate the gross profit.
Let's assume the original price of a portable computer is x dollars.
The 30 percent markup would increase the price by 30 percent of x, which is 0.3x.
So, the selling price of a portable computer after the 30 percent markup would be x + 0.3x = 1.3x dollars.
If the retailer expects to sell 100 portable computers at this price, the total revenue would be 100 * (1.3x) = 130x dollars.
Now, let's consider the case where the retailer increases the price by 10 percent instead of 30 percent. The selling price would now be x + 0.1x = 1.1x dollars.
Since the retailer still wants to maintain the same gross profit, the total revenue should be equal to 130x dollars.
To find the number of units the retailer needs to sell at the 10 percent increase in price to maintain the same gross profit, we need to solve the equation:
Number of units * Selling price = Total revenue
Number of units * 1.1x = 130x
Dividing both sides by 1.1x, we get:
Number of units = 130x / 1.1x
Simplifying, we have:
Number of units = 130 / 1.1
Number of units ≈ 118
Therefore, the retailer would need to sell approximately 118 units at a 10 percent increase in price to maintain the same gross profit.
Let the original cost price be 1000.
100 computers at 30% markup brings a profit of 100*(1000*30%)=30000
If the original price goes up 10% (cost =1100), the new profit per computer is 1300-1100=200
Number computers required to maintain the same total profit
= 30000/200=150