question_answer

A manufacturer considers that men and women workers are equally efficient and so he pays them at the same rate. He has 30 and 17 units of workers (male and female) and capital respectively, which he uses to produce two types of goods A and B. To produce one unit of A, 2 workers and 3 units of capital are required while 3 workers and 1 unit of capital is required to produce one unit of B. If A and B are priced at Rs. 100 and Rs. 120 per unit respectively, how should he use his resources to maximize the total revenue? Form the above as an LPP and solve graphically. What quality of manufacturer shown here.

Answer:

Let x units of A and y units of B are produced. Then LPP is Maximise\[Z=100x+120y\]subject to the constraints \[x\ge 0,\,\,y\ge 0\] \[2x+3y\le 30\] And                  \[3x+y\le 17\] Plotting the graph of in equations we notice, shaded portion represents the optimum solution. Feasible points for maximum revenue are\[A\,\left( \frac{17}{3},\,\,0 \right),\]\[B\,(3,\,\,8)\]and\[C\,(0,\,\,10)\].

Corner points	\[Z=100x+120y\]
\[A\,\left( \frac{17}{3},\,\,0 \right)\]	\[\frac{1700}{3}+0=566.67\]
\[B\,(3,\,\,8)\]	\[300+960=1260\](Maximum)
\[C\,(0,\,\,10)\]	\[0+1200=1200\]

Revenue is maximum at\[B\,(3,\,\,8)\], i.e. \[x=3,\]\[y=8\]. Hence, 3 units of A and 8 units of B must be produced to get maximum revenue of Rs. 1260. Value The manufactures consider man and women equally efficient which helps the growth of women in the society.