Question

To manufacture an automobile requires painting, drying, and polishing Epsilon Motor Company produces three types of cars, the Delta, the Beta, and the Sigma Each Delta requires 9 hours for painting. 4 hours for drying, and 3
hours for polishing A Beta requires 13 hours for painting, 6 hours for drying, and 4 hours for polishing, and a Sigma requires 9 hours for painting, 4 hours for drying, and 1 hour for polishing If the company has 257 hours for painting,
116 hours for drying, and 59 hours for polishing per month, how many of each type of car are produced?

Answer 1

Answer:

The company manufactures 5 Delta cars, 8 Beta cars and 12 Sigma cars.

Step-by-step explanation:

Let in the motor company x number of Delta cars, y number of Beta cars and z number of Sigma cars are manufactured.

So, from the condition given in the question we can write

9x + 13y + 9z = 257 ........ (1)

4x + 6y + 4z = 116 ........... (2) and  

3x + 4y + z = 59 ......... (3)

From equation (2) we get

9x + 13.5y + 9z = 261 ....... (4) {Multiplying with $\frac{9}{4}$ both sides}

Now, solving equations (1) and (4) we get

0.5y = 4

⇒ y = 8.

Now, from equation (2) putting the value of y we get,  

4x + 4z = 116 - 48 = 68

⇒x + z = 17 .......... (5)

Now, from equation (3) putting y = 8 we get,

3x + z = 59 - 32 = 27 ........ (6)

Hence, solving equations (5) and (6) we get, 17 - x = 27 - 3x

⇒ 2x = 10

⇒ x = 5  

So, z = 17 - x = 12

Therefore, the company manufactures 5 Delta cars, 8 Beta cars and 12 Sigma cars. (Answer)