$A$ vertical spring with force constant $K$ is fixed on a table. $A$ ball of mass $m$ at a height $h$ above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance $d$. The net work done in the process is

A company manufactures two types of screws $A$ and $B.$ All the screws have to pass through a threading machine and a slotting machine. A box of Type $A$ screws requires $2\, minutes$ on the threading machine and $3\, minutes$ on the slotting machine. A box of type $B$ screws requires $8\, minutes$ of threading on the threading machine and $2\, minutes$ on the slotting machine. In a week, each machine is available for $60\, hours.$ On selling these screws, the company gets a profit of $Rs.\, 100$ per box on type $A$ screws and $Rs.\, 170$ per box on type $B$ screws. Formulate this problem as a $LPP$ given that the objective is to maximise profit.