Current price is $100, current salesbare 5000 units. For every increase in price of $1, sales decrease by 20 units. Find optimum revenue.
To find the optimum revenue, we need to determine the price that maximizes the revenue. We can start by analyzing the relationship between price, sales, and revenue.
Given:
Current price (P) = $100
Current sales (S) = 5000 units
Price increase (ΔP) = $1
Sales decrease per price increase (ΔS) = 20 units
Revenue (R) is calculated by multiplying price with sales: R = P * S
To find the optimum revenue, we need to explore how revenue changes with different price levels. We'll start by increasing the price by $1 and observing the corresponding change in sales and revenue.
1. Price: $100, Sales: 5000 units, Revenue: $100 * 5000 = $500,000
2. Price: $101, Sales: 4980 units (sales decrease by 20 units), Revenue: $101 * 4980 = $502,980
3. Price: $102, Sales: 4960 units, Revenue: $102 * 4960 = $505,920
4. Price: $103, Sales: 4940 units, Revenue: $103 * 4940 = $508,820
We can continue this process and calculate the revenue for various price levels. However, this can be time-consuming. Instead, let's try to identify a pattern to find the optimal revenue more efficiently.
We can see that for each increase in price by $1, the sales decrease by 20 units. This implies that for every $1 increase in price, the revenue decreases by $1 * 20 = $20.
Since the current price is $100 with 5000 units sold, the initial revenue is $100 * 5000 = $500,000.
Now, let's determine the change in revenue for a $1 price increase:
Change in Revenue (ΔR) = ΔP * ΔS = $1 * 20 = $20
As we increase the price by $1, there is a $20 decrease in revenue. This means that to find the optimal revenue, we need to continue increasing the price until the revenue starts decreasing.
Since the revenue decreases by $20 for every $1 increase, we can determine the number of $1 price increases that can occur before the revenue decreases to find the optimal price.
Number of $1 price increases before decrease in revenue:
ΔR / ΔP = $20 / $1 = 20
This tells us that we can increase the price by $1 for a maximum of 20 times before the revenue starts decreasing. This implies that the optimal price occurs after 20 $1 increases from the current price.
Optimal price = Current price + 20 * ΔP
Optimal price = $100 + 20 * $1 = $120
Now, we can calculate the optimal revenue using the optimal price:
Optimal Revenue = Optimal Price * Sales
Optimal Revenue = $120 * 5000 = $600,000
Therefore, the optimum revenue is $600,000 when the price is set at $120.