A carpenter makes wooden chairs.
He has enough wood to make 30 chairs.
He makes $60 profit on a dining chair and $90 profit on a rocking chair.
It takes him 1 hour to make a dining chair and 2 hours to make a rocking chair.
He has only 40 hours available to work on the chairs.
The carpenter wants to maximize his profit given the constraints listed above. He draws the following graph to represent this situation.
The graph titled ‘Chair Profit Optimization’ shows the number of dining chairs made, from 0 to 50 in intervals of 5, along the x-axis and the number of rocking chairs made, from 0 to 50 in intervals of 5, along the y-axis. Two solid boundary lines are shown on the graph. The first boundary line has a y-intercept of (0, 20) and an x-intercept of (40, 0). The second boundary line has a y-intercept of (0, 30) and an x-intercept of (30, 0). The shaded region of the graph is below the point (0, 20) and the point of intersection of the two boundary lines (20, 10), and to the left of the x-intercept (30, 0).
Given the constraints, which statement is true?
A.
The carpenter can maximize profits by making 25 dining chairs and 5 rocking chairs.
B.
The carpenter can maximize profits by making 0 dining chairs and 20 rocking chairs.
C.
The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs.
D.
The carpenter can maximize profits by
making 30 dining chairs and 0 rocking chairs.
C. The carpenter can maximize profits by making 20 dining chairs and 10 rocking chairs.