question_answer

A shop-keeper deals in the sale of TV s and VCPs. He has 5.2 lacs to invest. He has only space for 50 pieces. ATV costs 20,000/- and a VCP costs 8,000/- From a TV and VCP he earns a profit of 1500/- and 800/- respectively. Assuming that he sells all the items that he purchases, the number of TVs and VCPs he should buy in order to Maximize his profit, is equal to

A) 60, 000

B) 55, 000

C) 51, 000

D) 47, 000  

Correct Answer: D

Solution :

[d] Let x and y denote the number of TV and VCP respectively. From the given data, we have \[x\ge 0,y\ge 0,x+y\le 50.\] he has 5.2 lacs to invest.

Hence \[20000x+8000y\le 520000.\]

The profit he earn is \[1500x+800y.\]Hence the LPP

Is maximize: \[z=1500x+800y\]

Subject to \[x\ge 0,y\ge 0,\]

\[x+y\le 50\] and \[5x+2y\le 130.\]

The boundary lines meet the coordinate axes at:

\[x-axis;(50,0),(26,0)\]

\[y-axis;(0,50),(0,65)\]

The boundary lines \[x+y=50\] and \[5x+2y=120\] intersect at \[(10,40).\]the feasible region is shown as shaded.

The quadrilateral has four vertices namely

\[0(0,0),A(26,0),B(10,40),C(0,65).\]The maximum occurs at \[B(10,40).\] Hence he should store 10 TVs and 40 VCPs. He earns a profit of

\[1500\times 10+800\times 40=47,000\]