the chair requires 1 hours of cutting, 2 hours of assembly, and 1 hour of finishing.
the table needs 2 hours of cutting, 1 hour of assembly, and 1 hour of finishing.
the maximum hours of cutting = 39 hours.
the maximum hours of assembly = 42 hours.
the maximum hours of finishing = 23 hours.
make a table as shown below:
chair table
number of x y
cutting hours 1 2 <= 39 hours
assembly hours 2 1 <= 42 hours
finishing hours 1 1 <= 23 hours
profit 20 30 maximize
your objective function is:
profit = 20x + 30y.
this is what you want to maximize.
your constraint functions are:
x + 2y <= 39
2x + y <= 42
x + y <= 23
using the desmos.com calculator, you would:
graph the opposite of the inequalities.
the maximum profit will be at the corners of the feasible region, which is the unshaded area of the graph.
evaluate the objective function at each ot these corner points.
the maximum profit is at the coordinate point of (7,16).
profit = 20*7 + 30*16 = 620
cutting hours = 1*7 + 2*16 = 39 <= 39
assembly hours = 2*7 + 1*16 = 30 <= 42
finishing hours = 1*7 + 1*16 = 23 >= 23
your solution is that he should make 7 chairs and 16 tables to maximize his profit and still be within the limits of the constraints.
the graphical solution looks like this:
