## Obtain the steady equation for the model M/M/1 : FIFO and derive the formula for

1. Average number of units in the queue.

2. Average waiting time of an arrival in the queue.

1. Average number of units in the queue.

2. Average waiting time of an arrival in the queue.

1. Economic Order quantity.

2. No. of oreders per year.

3. Time between two consecutive orders and

4. Optimal cost.

Player B

Player A $\begin{array}{cccc}{B}_{1}& {B}_{2}& {B}_{3}& {B}_{4}\end{array}\phantom{\rule{0ex}{0ex}}\begin{array}{c}{A}_{1}\\ {A}_{2}\\ {A}_{3}\\ {A}_{4}\end{array}\left[\begin{array}{cccc}3& 2& 4& 0\\ 3& 4& 2& 4\\ 4& 2& 4& 0\\ 0& 4& 0& 8\end{array}\right]$

Drink |
Plant G |
Plant J |

Drink A | 1300 | 1300 |

Drink B | 3000 | 1000 |

Drink C | 2000 | 5000 |

The market survey indicated that during the month of April, There will be a demand of 20,000 bottles of drink 'A', 40,000 bottles of drink 'B' and 44,000 bottles of drink 'C'. The operating costs per day of plants at 'G' and 'J' are 600 and 400 monetary units for how many days each plants be run in April so as to minimize the production cost. While so as to minimize the production cost. While still meeting the market demand? Solve by two-phase Simplex method.

$MinimizeZ={x}_{2}+3{x}_{3,}\phantom{\rule{0ex}{0ex}}Subjectto2{x}_{1}+{x}_{2}\le 2,\phantom{\rule{0ex}{0ex}}{x}_{1}+2{x}_{2}+6{x}_{3}\ge 5\phantom{\rule{0ex}{0ex}}-x1+{x}_{2}+2{x}_{3}=2,\phantom{\rule{0ex}{0ex}}{x}_{1},{x}_{2,}{x}_{3}\ge 0$