Question

Formulate the equations for the above problem.
($x$ and $y$ are the number of units of $A$ and $B$ manufactured in a day respectively)

• A. $15x+5y\le 10;24x+14y\ge 1000$
• B. $15x+5y\le 600;24x+14y\ge 1000$
• C. $5x+15y\le 600;24x+14y\ge 1000$
• D. $5x+15y\le 10;24x+14y\ge 1000$

Answer 1

Answer: (B)

$15x+5y\le 600;24x+14y\ge 1000$

Given, The profit from the product $A$ is $Rs.24$ and

The profit from the product $B$ is $Rs.14$

The maximum number of units of $B$ manufactured in a day is $30$

i.e., $y\le 30$ --------- (1)

Let the number of units of $A$ manufactured in a day be $x$

Therefore the profit for a day from the product $A$ is $24x$

Let the number of units of $B$ manufactured in a day be $y$

Therefore the profit for a day from the product $B$ is $14y$

The minimum profit for a day is $Rs.1000$

Therefore, the total profit from products $A$ and $B$ should be more than $Rs.1000$

i.e., $24x+14y\ge 1000$ --------- (2)

Given, time taken to manufacture one product of $A$ is $15min$ and

time taken to manufacture one product of $B$ is $5min$

Therefore, time taken to manufacture $x$ products of $A$ is $15xmin$ and

time taken to manufacture $y$ products of $B$ is $5ymin$

In a day, a worker works for a maximum of $10hrs=600min$

Therefore, the time taken to manufacture products $A$ and $B$ should be less than $600min$

I.e., $15x+5y\le 600$ --------- (3)