Predator / Prey Models

Part a) Given the following predator prey model where x(t) is the predator population and y(t) is the prey population: dx/dt = - ax + bxy + (z1)*x dy/dt = cy – gxy +(z2)*y Here both z1 and z2 can be positive or negative; parameters a, b, c, g are all defined to be positive. Parameters z1 and z2 can represent an external introduction of species at a constant rate (positive values) or an external harvesting of the species at a constant rate (a negative values). Under what conditions of z1 and z2 can the trivial fixed point (both species evolve to extinction) become stable (in both directions not a saddle node) Interpret these results. Part b) Giv... click for more

Martin Pullin Inventory Plan Calculations

I need your help in checking my caculation the attached inventory plan table for Martin-Pullin Bicycles Corp. My other calcualtions on the case are also included on the spreadsheet, I now need to calculate the inventory table, (there are two tabs on the spreadsheet). The key thing is to set up the inventory plan correctly, a month by month look at how many bicycles would be sold. Than I need to answer the following questions: Trace the inventory behavior with the forecasted demand (assume they are accurate and there are no forecasting errors) 1. Identify the amount of total stockout 2. Calculate the lost profit due to the stockout 3. Recalculate the total cost See attachm... click for more

Quantitative Methods - The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet.

I need help finding a solution to the below problems for Quantatitive Methods. 15. The production manager for the Whoppy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. The company operates one “8 hour” shift per day. Therefore, the production time is 480 minutes per day. During the production process, one of the main ingredients, syrup is limited to maximum production capacity of 675 gallons per day. Production of a regular case requires 2 minutes and 5 gallons of syrup, while production of a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case.... click for more

Waiting Line Models

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 9 minutes, there are three registration clerks, and guests arrive at the rate of one every 6 minutes, find a. Arrival and service rate. b. the probability all three clerks are idle. c. the probability a guest will have to wait. d. the average time a customer spends in the system. e. the average number of customers in line.

Linear Programming Problem

Max 8X + 7Y s.t. 15X + 4Y < 75 10X + 7Y < 70 X + Y < 8 X, Y > 0 a.Use a graph to show each constraint and the feasible region. b.Identify the optimal solution point on your graph.What are the values of X and Y at the optimal solution? c.What is the optimal value of the objective function?