Understanding how to use the Queing Theory - Erlang M/G/s/GD/s/infinity.

How do I solve a formula or equation for the Erlang System M/G/s/GD/s/infinity that predicts resource requirements (how many servers) using the known variables (1) new events per unit of time; (2) average time per event; (3) event time service level (must be resolved by duration); (4) percent of events that must meet that event time service level (duration).

Proving connectedness.

Prove that if G is a disconnected graph, the complement graph G^G is connected, and in fact, diam(G^)<=2.

Intro to OR class: Investment Problem

Al has $60,000 that he wants to invest now in order to use the accumulation for purchasing a retirement annuity in 5 years. After consulting with his financial adviser, he has been offered four types of fixed-income investments, which we will label as investments A,B,C, D. Investments A and B are available at the beginning of each of the next 5 years (call them years 1 to 5). Each dollar invested in A at the beginning of a year returns $1.40 (a profit of $.40) 2 years later (in time for immediate reinvestment). Each dollar invested in B at the beginning of a year returns $1.70 three years later. Investments C and D will each be available at one time in the future. Each dollar invested in ... click for more

OR Problem

Use the Simplex Tableau Method to solve the following linear programming problem. Maximise z=5x1 + 3x2 subject to: 4x1 + 2x2 <= 15 4x1 + x2 <= 10 x1 + x2 <=4 and xj >= 0, j =1,2. Use the optimal tableau above to answer the following. i) State the maximum value of z. ii) State the values of all the basic variables at the optimal point. iii) Write the objective function in terms of the non-basic variables. iv) Write each of the basic variables in terms of the non-basic variables. v) At the optimal point, which of the three constraints are active and which are inactive. Justify your answer.

Factory Operations Research Problem

A factory can assemble printers and scanners. The 50 factory workers operate three four hour shifts which keep the factory running for a total of 12 hours a day, 6 days a week. Before the printers and scanners can be assembled, the component parts must be purchased and the maximum value of the stock that can be held for a days assembly work is £1020. In the factory, a printer takes 1 hour 20 minutes to assemble using £20 worth of components whereas a scanner takes 30 minutes to assemble using £60 worth of components. The profit made on a printer is £10 and on a scanner is £15. a) Summarise the above information in a table b) Assuming that the factory can sell all the printers and sca... click for more