Question

You need to buy some filing cabinets. You know that Cabinet $X$ costs 10$perunit,requiressixsquarefeetoffloorspace,andholdseightcubicfeetoffiles.Cabinet$Y$costs$ $20$ per unit, requires eight square feet of floor space, and holds twelve cubic feet of files. You have been given 140$forthispurchase,thoughyoudo{n}^{\prime }thavetospendthatmuch.Theofficehasroomfornomorethan$72$ square feet of cabinets. How many of which model should you buy, in order to maximise storage volume. Write the maximum storage volume in the provided box.

Answer 1

Let number of X models be $x$

Let number of Y models be $y$

For floor $6x+8y=72$

or $3x+4y=36$

$10x+20y\le 140$

Volume $=8x+12y$

Now $x+2y\le 14$

Hence $2x+4y\le 28$

Volume $=8x+12y=8x+108-9x=108-x$

$2x+4y\le 28$

$2x+36-3x\le 28$

$36-x\le 28$

$x\ge 8$

So volume is maximum when $x$ is minimum $=8$

So volume $=108-8=100$