$1.$ Answer the following:

Define pay out time.

i$.$ Give two main electives of plant optimization.

$2.$ A project produces $120000$ units p$..$ year at $100\%$ capacity. The variable cost per unit is Rs $3$ and the fixed cost per year is Rs $10000.$ The selling price is Rs $5$ per unit. Find

$($i$)$ Annual Gross Profit. $($ii$)$ Net Profit if tax rate is $5\%,($iii$)$ BEP $($sales$).($iv$)$ BEP $($units$)$

$($b$)$ A rectangular storage container with an open top needs to have a volume of $10$m$^3.$ The length base is twice its with. Material for the base costs Rs $10$ per m$^2.$ Material for the sides costs Rs $6$ Find the cost of the material for the cheapest container.