Answer:
The number of cars that can be assembled in order to make maximum earnings is 6 cars
The number of cars that can be assembled in order to make maximum earnings is 4 cars
The maximum earnings = $2,100
Please find attached the graph of the system of equations
Explanation:
The given parameters are;
The amount earned for assembling a car = $250
The number of hours it takes to assemble a car = 3 hours
The number of workers needed to assemble a car = 3 workers
The amount earned for painting a car = $150
The number of hours it takes to paint a car = 2 hours
The number of workers needed to paint a car = 4 workers
The total number of hours available = 24 hours
The number of employees at work = 36 employees
Let the number cars assembled = X
The number of cars painted = Y
Therefore, we have;
The linear programming system is therefore;
3X + 4Y ≤ 36
3X + 2Y ≤ 24
X ≥ 0
Y ≥ 0
Y ≤ (36 - 3X)/4
Y ≤ (24 - 3X)/2
Graphing the function gives;
The amount earned for each car assembled = $250
The amount earned for each car painted = $150
Earnings, E = 250X + 150Y
Y = (-250/150)·X + E/150 = (-5/3)·X + E/150
Y = (-5/3)·X + E/150
Therefore the slope of the maximum earnings line is -5/3
Drawing several lines to find one that both passes through the feasible region and gives the highest y-intercept, gives the line that passes through the point (4, 6)
6 = (-5/3)·4 + E/150
From which we have E = 38/3.
Therefore, the auto shop supervisor should assemble 6 cars and paint 4 to earn E = $250 × 6 + $150 × 4 = $2,100.