A small business owner budgets $2,200$2,200 to purchase candles. The owner must purchase a minimum of 200200 candles to maintain the discounted pricing. If the owner pays $4.90$4.90 per candle to purchase small candles and $11.60$11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?
Question
A small business owner budgets 2,200 to purchase candles. The owner must purchase a minimum of 200200 candles to maintain the discounted pricing. If the owner pays 4.90 per candle to purchase small candles and 11.60 per candle to purchase large candles, what is the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing?
Solution
To solve this problem, we need to consider two constraints: the budget limit and the minimum number of candles to purchase.
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First, let's calculate the maximum number of large candles the owner can purchase with the budget of 2200 / $11.60 ≈ 189.66. Since we can't purchase a fraction of a candle, we round down to 189. This is the maximum number of large candles the owner can purchase if we only consider the budget.
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However, we also need to consider the minimum purchase requirement of 200 candles. If the owner purchases 189 large candles, they would not meet this requirement. Therefore, the owner needs to purchase some small candles as well.
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To maximize the number of large candles, we should minimize the number of small candles. Since each small candle costs $4.90, the owner can purchase the remaining candles as small ones to meet the minimum requirement.
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The difference between the minimum requirement and the number of large candles is: 200 - 189 = 11. So, the owner needs to purchase at least 11 small candles.
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The cost of 11 small candles is: 11 * 53.90. Subtract this from the total budget to see how much is left for large candles: 53.90 = $2146.10.
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Now, divide this remaining budget by the cost of one large candle to find the maximum number of large candles the owner can purchase: 11.60 ≈ 185.01. Again, we can't purchase a fraction of a candle, so we round down to 185.
So, the maximum number of large candles the owner can purchase to stay within the budget and maintain the discounted pricing is 185.
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