The FlameyWamey Company FWC produces extinguishers and heat

The Flamey-Wamey Company (FWC) produces extinguishers and heat detectors. Each extinguisher takes three hours of labor from the materials department and four hours of labor from the contruction department. Each heat detector requires three hours of materials and two hours of construction. During the current week, 120 hours of materials time are available and 150 hours of construction time. Each extinguisher produced gives a profit of £12 and each heat detector a profit of £10. How many heat detectors and extinguishers should be made?

Solution

Let x no. extinguishers and y no. heat detectors

Each extinguisher takes three hours of labor from the materials department and four hours of labor:

3x , 4x

Each heat detector requires three hours of materials and two hours

3y , 2y

20 hours of materials time are available and 150 hours of construction time

3x+3y = 120 -----(1)

4x +2y = 150 -------(2)

Profit = 12x +10y

There is no information about whether the criteria is to maximise the profit or not .

We can solve the two variable equation to get the no, of heat detectors and extinguishers

3x+3y = 120 -----(1)

4x +2y = 150 -------(2)

On solving the two equations we get :x = 35 no. extinguishers ; y=5 no. heat detectors

Please specify if any other requirement is given .