Answer to Question #287010 in Management for fayisa arba

Question

 LIFAN Motors PLC. produces different models of automobiles and supply for domestic market. automobile products, namely Model-1 and model 2 . Therefore, the production division has information, which is related to the production and supply of these two model automobiles to satisfy their potential customers. In addition to this, to produce each model of automobiles there are three different operational stages; Designing, Assembling and Testing. The sales price of each model-1 automobile is $500 to make, while the sales price of each model-2 automobile is $800. Furthermore, the following information is obtained from the production division of the company. Finally, the company wishes to determine its weekly product mix to maximize its profit.

Models

Hours required for each Operation

Designing

Assembly

Testing

Model-1

10

20

5

Model-2

15

25

10

Total Available Hours

100

600

30

.

Determine how many units of each model automobiles should be produced by the LIFAN Motors to 

Answer 1

Let X represent model 1

Let Y represent model 2

Product Design hrs Assembly hrs Test hrs$=$ Selling price

X 10hrs 20hrs 5hrs$=$ $500

Y 15hrs 25hrs 10hrs$=$ $800

Total Hrs $=$ 100hrs 600hrs 30hrs

10x $+$ 15y$=$ 100

5x $+$ 10y $=$ 30

x $+$ 2y $=$ 15

x $=$ 15$-$ 2y

10$($ 15$-$ 2y$)$ $+$ 15y $=$ 100

150$-$ 20y$+$ 15y$=$ 100

150$-$100$=$ 5y

50$=$ 5y

y$=$ 10

x $=$ 15$-$ 2y

x$-$ 2y$=$ 15

x$-$ 2$(10)$ $=15$

x$-20=15$

x$=35$

Therefore, 35 units of model 1 and 10 units of model 2 will be required