MATH SOLVE

3 months ago

Q:
# An online furniture store sells chairs for $200 each and tables for $600 each. Every day, the store can ship a maximum of 32 pieces of furniture and must sell no less than $12000 worth of chairs and tables. If 13 chairs were sold, determine the minimum number of tables that the the store must sell in order to meet the requirements. If there are no possible solutions, submit an empty answer.

Accepted Solution

A:

Answer: If the minimum 13 chair were sold , then the minimum number of Table sold is 14Step-by-step explanation:Given as :The cost of each chair = $ 200The cost of each table = $ 600The total number of furniture sold per day = 32The minimum amount of selling per day = $ 12000Let the total number of chair = CThe total number of table = TSo , according to questionC + T = 32 .......1200 C + 600 T = 12000 .......2Solving eq 1 and 2200 C + 600 T = 12000200 × ( C + T ) = 32 × 200I.e 200 C + 200 T = 6400or, ( 200 C + 600 T ) - ( 200 C + 200 T ) = 12,000 - 6400Or, 400 T = 5600∴ T = [tex]\frac{5600}{400}[/tex]I.e T = 14Put The value of T in eq 2So, 200 C + 600 × 14 = 12000 or , 200 C + 8400 = 12,000Or, 200 C = 12000 - 8400Or, 200 C = 3600∴ C = [tex]\frac{3600}{200}[/tex]I.e C = 18 The number of chair sold is 18 If the number of chair sold is 13 ,Then the min number of table sold = 200 × 18 + 600 T = 12000i.e 600 T = 12000 - 3600or, 600 T = 8400∴ T = [tex]\frac{8400}{600}[/tex]I.e T = 14Hence if the minimum 13 chair were sold , then the minimum number of Table sold is 14 . Answer