Question

Juan sells 2 sizes of dried wreaths it takes him 3 hours to make each large and 2 hours to make each small one. he has material for no more than 6 large wreaths or 9 small wreaths. he can work no more than 24 hours. what are 2 possible combinations of large and small wreaths

Answer 1

Answer:  The answer is (2,9) and (6,3).

Step-by-step explanation: Given that Juan sells 2 sizes of dried wreaths. He takes 3 hours to make each large one and tales 2 hours to make each small one. Also, he has material for maximum 6 large wreaths or maximum 9 small wreaths.

Let, 'x' and 'y' be the number of number of large wreaths and number of small wreaths respectively made by Juan.

So, according to the given information, we have the following relations -

$3x+2y\leq 24,~~x\leq 6,~~y\leq 9.$

We tried plotting these inequalities in the graph paper (please see the attached figure), and found that the following two solutions will fit the situation perfectly.

Point A (x = 2, y = 9)   and   point B (x = 6, y = 3).

Thus, the two possible combinations are

(i) 2 large wreaths and 9 small wreaths, and

(ii) 6 large wreaths and 3 small wreaths.