Question

One unit of product $P_1$ requires 3 kg of resource $R_1$ and 1 kg resource $R_2$. One unit of product $P_2$ requires 2 kg of resource $R_1$ and 2 kg of resource $R_2$. The profits per unit by selling product $P_1$ and $P_2$ and Rs. 2000 and Rs. 3000 respectively. The manufacturer has 90 kg of resource $R_1$ and 100 kg of resource $R_2$.

The manufacturer can make a maximum profit of Rs.

• A. 200000
• B. 135000
• C. 60000
• D. 150000

Answer 1

The correct option is B 135000

$\text{For product:}$

$P_1=3kg\text{of}{R}_1\text{and}1kg\text{of}{R}_2\text{is required.}$

$\text{For product:}$

$P_2=2kgof{R}_1\text{and}2kgof{R}_2\text{is required.}$

$\text{Profit by selling}{P}_1=Rs.2000$

$\text{Profit by selling}{P}_2=Rs.3000$

$R_1=90kg$

$R_2=100kg$

$\text{Maximum profit,}Z=2000P_1+3000P_2$

$\text{Subjected to:}$

$3P_1+2P_2\le 90$

$P_1+2P_2\le 100$


$\text{Hence, resource}{R}_2\text{is redundant.}$

$\text{Profit,}{Z}_{(30,0)}=2000\times 30+3000\times 0=Rs.60000$

$Z_{(0,45)}=2000\times 0+3000\times 45=Rs.135000$