MHB Maximize City Kid Earnings: Peas & Carrots

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To maximize earnings from a 12x5 inch windowsill, the focus is on growing carrots, which yield $50 per set compared to $15 for peas. The space allows for a maximum of 12 sets of carrots, generating a total of $600, while using all space for peas would only yield $225. Given the constraints of space and the number of sets possible, prioritizing carrots is the most profitable strategy. The discussion emphasizes the importance of utilizing the available space efficiently to maximize income. Therefore, planting only carrots is recommended for optimal earnings.
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I am a city kid with a windowsill with the dimensions 12x5 inches. I have peas which require a 1x4 space and make me 15 dollars, and carrots which require 1x5 space and make me 50. I can only make 15 sets of peas if I were to use the whole space, and 12 sets of carrots if I were to use the whole space for carrots. How would I make the most amount of money? I think I have to use graphing and I know the restrictions are x+y ≤ 60 (60 slots available), and x≤15 (peas) and y≤12 (carrots).
 
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zarahzehri01 said:
I am a city kid with a windowsill with the dimensions 12x5 inches. I have peas which require a 1x4 space and make me 15 dollars, and carrots which require 1x5 space and make me 50. I can only make 15 sets of peas if I were to use the whole space, and 12 sets of carrots if I were to use the whole space for carrots. How would I make the most amount of money? I think I have to use graphing and I know the restrictions are x+y ≤ 60 (60 slots available), and x≤15 (peas) and y≤12 (carrots).

Hi zarahzehri01! Welcome to MHB! (Smile)

If we use all available space for peas, we'd make $15 \times \$15 = \$225$.
And if we use all available space for carrots, we'd make $12 \times \$50 = \$600$.
So if we can, we should put only carrots in the windowsill.
Can we?
 
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