Tasty Yogurt Manufacturing Co. makes 10 cents per container of plain yogurt that it sells and 12 cents per container of vanilla yogurt. They want to make a monthly profit of at least $3,200. This month, Tasty expects to sell at least 12,000 cups of plain yogurt (p), but no more than 15,000 cups of vanilla yogurt (v).

Question

Fill in the Blank Question
If Tasty sold exactly 15,000 cups of vanilla yogurt, how many cups of plain yogurt will the company need to sell to meet their profit goal of at least $3,200?
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Answer 1

To find out how many cups of plain yogurt (p) Tasty Yogurt Manufacturing Co. needs to sell to meet their profit goal of at least $3,200, we can use the profit formula:

\[ \text{Profit} = (\text{Profit per plain yogurt}) \times p + (\text{Profit per vanilla yogurt}) \times v \]

Given:

• Profit per container of plain yogurt = $0.10
• Profit per container of vanilla yogurt = $0.12
• Desired profit = $3,200
• Number of cups of vanilla yogurt sold (v) = 15,000

Plugging in the values:

\[ 3200 = 0.10p + 0.12(15000) \]

Calculating the profit from the vanilla yogurt:

\[ 0.12 \times 15000 = 1800 \]

Now substitute back into the profit equation:

\[ 3200 = 0.10p + 1800 \]

Next, isolate \(0.10p\):

\[ 3200 - 1800 = 0.10p \]

\[ 1400 = 0.10p \]

Finally, solve for \(p\):

\[ p = \frac{1400}{0.10} = 14000 \]

Thus, Tasty Yogurt Manufacturing Co. needs to sell 14,000 cups of plain yogurt to meet their profit goal of at least $3,200 if they sold exactly 15,000 cups of vanilla yogurt.