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- A local coffee shop in its busy period gets about 10 customers per minute. A typical serverworking at the counter can help customers at a rate of 2 per minute.4(a). [2pts] What is the minimum number of servers the shop needs to have to make this astable system, i.e. rho < 1?4(b). [10pts] We will assume that the server’s rate of service stays constant. However, therate at which customers come in might fluctuate. Consider customer arrival rates rangingfrom 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number ofservers the shop should have during its busy period. Range the number of servers fromyour answer in 4(a) up to 5 more (that is, if you said x in (a), let c = x, x+1,…,x+5)Create simultaneous line plots similar to what was done in the M/M/c practice for thevalues of R0. Plot the c values on the x-axis and create a separate line plot for each value oflambda(customer arrival rate). Give the appropriate titles and labels and include a legend.Make sure each…An automated machine dispenses milkshakes into large-size cups at a local fast food chain. The amount dispensed is normally distributed or N(23,1.4), all measures in ounces. If the cups can hold a maximum of 25 ounces, and 700 milkshakes are sold on a particular day, about how many of the milkshakes will overflow?Consider the following system of tanks. Each tank initially contains V1 = 200 gallons and V2 = 300 gallons of fresh water. At time t = 0 minutes, all three valves open up, allowing for a salt brine solution (at a concentration of 2 lbs/gal) to enter the first tank through the first valve. At the same time, the solution is allowed to pass from the first tank into the second tank, and finally, the solution is allowed to exit the second tank, all at the same rate of r = 5 gal/min. (a) Set up a system of differential equations that will allow you to solve for q1(t) and q2(t), which represent the amount of salt (in pounds) in tank 1 and tank 2, respectively, at time t. (b) Solve your system to find q1(t) and q2(t), and then graph them
- The table shows the recipe and the available ingredients for making the maximum possible number of sandwiches. Making Sandwiches Recipe for One Sandwich Total Ingredients Available 2 tomato slices, 4 cucumber slices, 2 bread slices 8 tomato slices, 22 cucumber slices, 8 bread slices If the ingredients represent reactants of a chemical reaction, which of the following represents the leftover reactant? Six cucumber slices Four cucumber slices Four tomato slices or Six tomato slicesFor the system below, analyze the convergence of the iterative Gauss-Jacobi method and apply this method (swap lines, if necessary) to find an approximation of the solution of the system, with ε = 10−2Solve 4x - 3y = 6 for y and graph it on a graphingutility with a standard window.
- Customers arrive at the ticket counter of a local movie theater at a rate of 240 persons per hour, at 5.30 PM. After 10 minutes, the arrival rate declines to 60 persons per hour and continues at that level for 20 minutes. If the service rate is 2.5 persons/minute. (3)a.Describe the performance of the system, assuming that all the factors remain the same. (Longest queue, longest delay, total delay, average delay/person, etc.)b.Draw a neat sketch of the system. (Apply the D/D/1 model)James has two job offers. Massy offers James the job with an initial annual salary of $38,800.00 along with guaranteed annual increases of $3,200.00 for the first five years. Unicomer offers him an initial annual salary of $47,600.00 along with guaranteed annual increases of $1,000.00 for the first five years. a. Compare and contrast the two offers to determine the company that offers the highest annual salary for the fifth year of employment. Show all necessary calculations. b. Compare and contrast the two offers to determine the company that proposes the most (total) renumeration over James’ first five years of employment. Show all necessary calculations. c. Which company should James take up his employment with if both companiesoffer him an annual salary of $60,000.00 in his sixth year? Why?A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? I need to use the Five Step Method for mathematical modeling. Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency. Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math. Formulate the model. Restate…
- A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? I need to use the Five Step Method for mathematical modeling. Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency. Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math. Formulate the model. Restate…A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? I need to use the Five Step Method for mathematical modeling. Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency. Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math. Formulate the model. Restate the…A local coffee shop in its busy period gets about 10 customers per minute. A typical serverworking at the counter can help customers at a rate of 2 per minute. 4(a). What is the minimum number of servers the shop needs to have to make this astable system, i.e. rho < 1? 4(b). We will assume that the server’s rate of service stays constant. However, therate at which customers come in might fluctuate. Consider customer arrival rates rangingfrom 8 per minute to 12 per minute. Conduct a sensitivity analysis on the number ofservers the shop should have during its busy period. Range the number of servers fromyour answer in 4(a) up to 5 more (that is, if you said x in (a), let c = x, x+1,…,x+5) Create simultaneous line plots similar to what was done in the M/M/c practice for thevalues of R0. Plot the c values on the x-axis and create a separate line plot for each value oflambda(customer arrival rate). Give the appropriate titles and labels and include a legend. Make sure each graph is clear…