A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to?

produce, and the wreaths take 2 hours.  The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week.  Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths.  Then graph the system of inequalities





Could someone show me how to solve and how graph this please? Thank you!

A small company produces both bouquets and wreaths of dried flowers.  The bouquets take 1 hour of labor to?
The first restriction is labor time. As it takes 1 hour to make a bouquet and 2 to make a wreath, the total amount of hours spent to make x bouquets and y wreaths is x + 2y.





As the labor is limited to 80 hours, x + 2y ≤80. This is a linear line, so you only need to know two points to sketch it. When x = 0, it crosses the y axis, so 2y = 80, y = 40, one point lies at (0,40). When y = 0, x = 80, so the other point is at (80,0). Connect the two points for your first line.





The other restriction is the number of items. As bouquets and wreaths are both single items, the total number of items is simply x + y. As this must be less than or equal to 60, we can say that x + y ≤60.





The points for this line are found in a similar manner. x = 0 gives y = 60 and a point (0,60). y = 0 gives x = 60 and a point (60,0). Connect these two for you other line.





As both equations are less then or equal to the constant, the range of all possible work is the area below both lines (not going past the axes as you can't get negative amounts of items).
Reply:let b be the numbers of bouquets and w be the number of wreaths





the company will not produce no more than 60 items


b + w ≤ 60





the rate to produce a bouquet is 1 bouquet/hr.


the rate to produce a wreath is 1 wreath/2hr = .5 wreath/hr





item 1 /rate + item 2 / rate ≤ time





b/1 + w/.5 ≤ 80





the answer is:


b + w ≤ 60


b + 2w ≤ 80

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