Question 20

Explanation

We will calculate the normal income first, then determine the new price and new sales quantity so that the income remains the same but sales increase.

Calculating Normal Income

Normal income ($I_{\text{normal}}$) is:

Determining Relationship between Price and New Sales

Let $x$ be the number of price reductions of $\text{Rp}1,000.00$.

• New Price: $H = 12,000 - 1,000x$
• New Quantity Sold: $J = 200 + 20x$

We want the income to remain the same ($\text{Rp}2,400,000.00$):

We simplify by dividing the factors (e.g., divide by $1,000$ on price and by $20$ on quantity):

We obtain two solutions:

1. $x = 0$ (Normal condition, no change)
2. $x = 2$ (Price reduction occurs)

Since the shop owner wants to increase sales, we choose $x = 2$.

Calculating Number of Iced Coffees Sold

Substitute $x = 2$ into the new quantity formula:

So, the number of iced coffees sold is 240 cups.