Please show the equations that are used to get solutions

1. The Soft Toys Company has collected information on fixed and variable costs for four potential plant locations.

Location	Annual Fixed Cost ($)	Unit Variable Cost ($)
A	200,000	50
B	300,000	45
C	400,000	25
D	600,000	20

a. Plot the total cost curves for the four plant locations on a single graph.

b. Find the break-even points and determine the range of demand for which each location has a cost advantage.

c. The sales manager predicts that demand will be 30,000 units. Which facility is best for the predicted demand?

2. The Bruhaha Brewery is planning to build another brewery for the expanding U.S. market. The company has identified five critical location factors and their relative weights. The scores for each of the three potential sites are shown in the following table. Which site should be selected for the new brewery?

Critical Location Factors	Factor Weight (Sum to 1)	Columbus Scores (1-100)	Las Vegas Scores (1-100)	Spokane Scores (1-100)
Labor Cost	0.15	70	90	50
Proximity to market	0.25	100	90	80
Supplier base	0.20	80	100	70
Quality of life	0.30	90	60	60
Taxes	0.10	60	80	90

3. For the previous month, the Bichsel Lounge served 1,500 customers with very few complaints. Their labor cost was $3,000; material cost was $800; energy cost was $200; and the building's lease cost was $1,500. They were open twenty-six days during the month, and the lounge has twenty seats. They are open six hours per day, and the aver- age customer stay is one hour.

a. Calculate the single-factor productivities and the overall multiple-factor productivity. How could they improve the productivity?

b. Calculate the monthly capacity and the capacity utilization.

4. Given an average service rate of twelve customers per hour, what is the probability the business can handle all the customers when the average arrival rate is ten customers per hour? Use the Poisson distribution to calculate the probabilities for various customer arrivals.

5. Theresa can handle about ten customers per hour at her one-person comic bookstore. The customer arrival rate averages about six customers per hour. Theresa is interested in knowing the operating characteristics of her single-channel, single-phase queuing system.

6. How would Theresa's queuing system operating characteristics change for the problem above if she added another cashier and increased her service rate to twenty customers per hour?