Question

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Model Problem
Coffee vs. Tea
A café by Lindsay's house sells coffee and tea. They are trying to make the most amount of money
possible. In other words they are trying to maximize profit. They asked me to look at their sales
receipts and figure out what they should do. But they had a few limitations on what could be done.
Constraint #1: The Baristas (the people who makes the coffee) can only reasonably serve 90 cups
per shift. It can be 90 cups of coffee, 90 cups of tea or a mixture of the two.
Constraint #2: Coffee costs $3 per cup and Tea costs $2. In order to stay on track to pay their
bills, the owners would like to sell at least $120 worth of beverages every shift.
Constraint #3: They have a limited supply of coffee and tea that gets delivered every day. If they
don't want to sell out (And annoy customers) they can sell no more than 70 cups of tea per shift.
Constraint #4: Similar to the last constraint, they can only sell 60 cups of coffee per shift before
they sell out.
Question: How much tea and how much coffee should they sell every shift in order to maximize
profits? They make $1.10 on each cup of coffee and $.90 on each cup of tea.

Answer 1

The café should sell 60 cups of coffee and 30 cups of tea per shift to maximize profits, which gives a total profit of $93 while adhering to all constraints.

Step-by-step explanation:

To maximize profits, the café needs to determine the optimal mix of coffee and tea to sell within their constraints. The profit per cup is $1.10 for coffee and $0.90 for tea. To meet the minimum sales target of $120 and not exceed the baristas’ serving limit of 90 cups per shift, nor the limited supply of 70 teas and 60 coffees, we can set up inequalities:

• For barista serving limit: C + T ≤ 90 (where C is coffee and T is tea)
• For minimum sales: $3C + $2T ≥ $120
• For tea supply limit: T ≤ 70
• For coffee supply limit: C ≤ 60

Now, we calculate the maximum profit considering the supply constraints and the profit margins. Selling 60 cups of coffee would yield $66 (60 x $1.10), and 30 cups of tea would yield $27 (30 x $0.90), summing to $93 in profit, which also meets the sales target.

Thus, the café should sell 60 cups of coffee and 30 cups of tea to maximize profits while satisfying all constraints.

Answer 2

coffee is the best answer in my mind