A small manufacturing company produces child-sized and adult-sized adirondack chairs. The company makes a profit of $40 on each child-sized chair and $75 on each adult-sized chair. The manufacturer can make a total of 150 chairs per week. It takes 1 hour of labor to make a child-sized chair and 2 hours of labor to make an adult-sized chair, and the company has 200 hours of labor available per week. Let x represent the number of child-sized chairs and y represent the number of adult-sized chairs. Determine how many child-sized and adult-sized adirondack chairs should be manufactured weekly to maximize production. A: 100 child-sized chairs and 50 adult-sized chairs B: 150 child-sized chairs and 0 adult-sized chairs C: 50 child-sized chairs and 100 adult-sized chair D: 0 child-sized chairs and 100 adult-sized chairs
A small manufacturing company produces child-sized and adult-sized adirondack chairs. The company makes a profit of $40 on each child-sized chair and $75 on each adult-sized chair. The manufacturer can make a total of 150 chairs per week. It takes 1 hour of labor to make a child-sized chair and 2 hours of labor to make an adult-sized chair, and the company has 200 hours of labor available per week. Let x represent the number of child-sized chairs and y represent the number of adult-sized chairs.
Determine how many child-sized and adult-sized adirondack chairs should be manufactured weekly to maximize production.
A: 100 child-sized chairs and 50 adult-sized chairs
B: 150 child-sized chairs and 0 adult-sized chairs
C: 50 child-sized chairs and 100 adult-sized chair
D: 0 child-sized chairs and 100 adult-sized chairs
Let Company produces (x) child size chairs and (y) adult size chairs.
Therefore,
Total number of chairs , = x + y
Total profit , P = 40x + 75y
Total time , T = 1x + 2y
Given that company can make maximum 150 chairs per week. So, Total number of chairs should be less that 150.
It is given that company have maximum of 200 hours of labor work. So, Total time should be less that 200.
Now, we will maximize the Profit by using Critical points which will be find by plotting the inequalities on graph.
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