SOLUTION: The Star Electronics Company produces two robotic vacuums. The production process for each product is similar in that both require a certain number of hours of electronic work and

Question 1199297: The Star Electronics Company produces two robotic vacuums. The production process for each product is similar in that both require a certain number of hours of electronic work and a certain number of labour hours in the assembly department. Robotic vacuum A takes 4 hours of electronic work and 2 hours in the assembly shop. Robotic vacuum B requires 3 hours in electronics and 1 hour in assembly. During the current production period, 240 hours of electronic time are available, and 100 hours of assembly department time are available. Each robotic vacuum A sold yields a profit of RM 700 while each robotic vacuum B produced may be sold for a RM 500 profit.
Formulate a linear programming model for this problem.
a) Find the objective function
b) Identify the variable and list all the constraints
c) Calculate the intersection point.
d) Draw the graph with a complete label of the axis, intersection point, line equation, and shaded region.
e) Find the optimal solution

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = number of type A robotic vacuums.
y = number of type B robotic vacuums.

objective function is profit = 700x + 500y
this is what you want to maximize.

constraint functions are:

4x + 3y <= 240 for electronics work hours.
2x + y = 100 for assembly hours.
x >= 0
y >= 0

the chart that i made up is shown below:

                              type A        type B
electronics work hours           4             3        <= 240
assembly hours                   2             1        <= 100
profit                         700           500        maximize

using the calculator at https://www.desmos.com/calculator, you would graph the opposite of the inequalities.
the are of the graph that is not shaded is your region of feasibility.
your maximum profit will be at the corner points of this region.
the corner points on the graph are in (x,y) format.
x represents the number of type A vacuums.
y represents the number of type B vacuums.

here's what the graph looks like.

the maximum profit is at (30,40) = 41,000
total electronics hours = 240
total assembly hours = 100
all constraints were met.

let me know if you have any quetions.
theo

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