Instructions

CO$-3$: Identify the various manufacturing and service system designs and capacity planning methods.

The manager of an oil refinery must decide on the optimal mix of two possible blending processes of which the input

and output per production run are given as follows:

The maximum amount available of crude A and $B$ are $200$ units and $150$ units respectively. Market requirements show that

at least $100$ units of gasoline $x$ and $80$ units of gasoline $Y$ must be produced. The profit per production run from process $1$

and process $2$ are Rs$.300$ and Rs$.400$ respectively. Formulate this problem as a linear programming model.

A city police department has the following minimal daily requirement for policeman. Note. you are to consider period $1$

as following immediately after period $6.$ Each policeman works eight consecutive hours. Let $x$ denote the number of men

starting work in period $t$ everyday. The police department seeks a daily manpower schedule that employs the least

number of policemen, provided that each of the above requirements is met. Formulate linear programming model to find

an optimal schedule.

A car dealer selects his cars for sale very carefully so as to ensure the optimization of his profits. He deals in $4$ types

of cars A$,$ B$,$ F and G$.$ The purchase value of the cars range at Rs$.60,000,150,000,55,000$ and $220,000$ and the sales

value is fixed at Rs$.80,000,175,000,75,000$ and $250,000$ respectively. The probability of sale are $0\mathrm{.}8,0\mathrm{.}9,0\mathrm{.}6$ and $0\mathrm{.}50$

respectively during a period of six months. In order to invest Rs$.20,00,000$ in his deals, he wishes to maintain the rates

of purchase of cars as $3$:$1$:$2$:$4.$ Work out how and how much he should buy. Formulate this problem as LP model.

Use graphical method to solve the following LP problems

Max. $Z=3x_1+4x_2$

Subject to

$2x_1-x_{2}10$

$x_1-5x_{2}12$

$x_1-x_{2}6$

$x_1{x}_{2}0$