Air enters a counter-flow heat exchanger at $${7^ \circ }C$$ and leaves at $${40^ \circ }C$$. Water enters at $${30^ \circ }C$$ and leaves at $${50^ \circ }C$$. The $$LMTD$$ in deg $$C$$ is

A company places orders for supply of two items $$A$$ and $$B.$$ The order cost for each of the items is Rs.$$300$$ /order. The inventory carrying cost is $$18\% $$ of the unit price per year per unit. The unit prices of the items are Rs.$$40$$ and Rs.$$50$$ respectively. The annual demands are $$10,000$$ and $$20,000$$ respectively.

(a) Find the economic order quantities and the minimum total cost
(b) A supplier is willing to give a $$1\% $$ discount on price, if both the items are ordered from him and if the order quantities for each item are $$1000$$ units or more. Is it profitable to avail the discount?

Given below are the data for a project network.
(a) Draw the network for the above project capturing the precedence relationships.
(b) Find the critical path and its duration.

In a time series forecasting model, the demand for five time periods was $$10, 13,$$ $$15,$$ $$18$$ and $$22.$$ A linear regression fit resulted in an equation $$F = 6.9 + 2.9$$ $$t$$ where $$F$$ is the forecast for period $$t$$. The sum of absolute deviations for the five data is