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. $\newline$ Answer:

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Q. 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.

\newline

Answer:

Identify Constraints: Identify the constraints of the problem. $\newline$ 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. $\newline$ Since each chair costs $\$100$ and $20$ chairs were sold, we multiply the number of chairs by the cost per chair. $\newline$ Total value of chairs = $20$ chairs * $\$100$ /chair = $\$2000$ .
Determine Remaining Amount: Determine the remaining amount needed to reach the sales requirement. $\newline$ 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. $\newline$ Remaining amount = $\$5800 - \$2000 = \$3800$ .
Calculate Maximum Tables: Calculate the maximum number of tables that can be sold to meet the remaining sales requirement. $\newline$ 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. $\newline$ Maximum number of tables = $\$3800 / \$350/\text{table} \approx 10.857$ tables. $\newline$ Since we cannot sell a fraction of a table, we round down to the nearest whole number. $\newline$ 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. $\newline$ Total pieces of furniture shipped = number of chairs sold + number of tables sold. $\newline$ Total pieces of furniture shipped = $20$ chairs + $10$ tables = $30$ pieces. $\newline$ 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. $\newline$ 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.