a library has to accomodate two types of books on a shelf the books are 6cm and 4cm thick - Maths - Linear Programming

Question

a library has to accomodate two types of books on a shelf the
books are 6cm and 4cm thick and weigh 1kg and 3/2kg the shelf is
96cm long and atmost can support a weight of 21kg how should the
sgelf be filled with the books of two types in order to include the
greatest number of books? make it as an L P P and solve it
graphically

Ayush Jha · Accepted Answer

Let the number of books be x and y

Since the total length of the self is 96 cm. So,

$6 x + 4 y = 96 \Rightarrow 3 x + 2 y = 48$ .......(1)

Since the total weight the book shelf can accommodate is 21 kg. So,

$x + \frac{3}{2} y = 21 \Rightarrow 2 x + 3 y = 42$ .......(2)

We can simply get the answer by solving the above two linear equations to get,

x = 12

y = 6

But to solve it using linear programing your need to plot the linear equations mentioned in the equation (1) and (2). The point of intersection of the two linear equation will give the solution. The graph would look like-