An online furniture store sells chairs for $100 each and tables for $350 each. Every day, the store can ship at most 33 pieces of furniture and must sell at least $5800 worth of chairs and tables. If 20 chairs were sold, determine the maximum number of tables that the store could sell that would meet the requirements. Answer:

Question

An online furniture store sells chairs for  $100 each and tables for  $350 each. Every day, the store can ship at most 33 pieces of furniture and must sell at least  $5800 worth of chairs and tables. If 20 chairs were sold, determine the maximum number of tables that the store could sell that would meet the requirements. Answer:

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Identify Constraints: Identify the constraints of the problem. The store can ship at most 33 pieces of furniture and must sell at least $5800 worth of chairs and tables. We also know that 20 chairs have already been sold.Calculate Chair Value: Calculate the total value of the chairs sold. Since each chair costs $100 and 20 chairs were sold, we multiply the number of chairs by the cost per chair. Total value of chairs = 20 chairs * $100/chair = $2000.Determine Remaining Amount: Determine the remaining amount needed to reach the sales requirement. The store needs to sell at least $5800 worth of furniture. Subtract the total value of the chairs from this amount to find out how much more needs to be sold in tables. Remaining amount = $5800 - $2000 = $3800.Calculate Maximum Tables: Calculate the maximum number of tables that can be sold to meet the remaining sales requirement. Since each table costs $350, divide the remaining amount by the cost per table to find the maximum number of tables that can be sold. Maximum number of tables = $3800 / $350/table ≈ 10.857 tables. Since we cannot sell a fraction of a table, we round down to the nearest whole number. Maximum number of tables = 10 tables.Check Shipping Limit: Check if the total number of pieces of furniture shipped does not exceed the shipping limit. Total pieces of furniture shipped = number of chairs sold + number of tables sold. Total pieces of furniture shipped = 20 chairs + 10 tables = 30 pieces. Since 30 pieces is less than the shipping limit of 33 pieces, the shipping constraint is satisfied.Verify Solution: Verify that the solution meets all the constraints. The store has sold 20 chairs and can sell a maximum of 10 tables without exceeding the shipping limit and while meeting the sales requirement. Therefore, the solution is valid.

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