If x1 and x2 are the factors of production of a typical firm, output price is p, price of x1 and x2 are w1 and w2, respectively and the firm’s production function is:

           f (x1, x2) = x1^3 x2^3

i. Write up firm’s short run and long run profit maximization problem. Show firm’s short run profit maximization graphically please.

ii. Using the information above can you write the cost minimization problem for this firm if the firm decides to produce y1 level of output? Please show graphically how the firm minimizes its costs. What is the alternative method we can use to find the optimal quantity of x1 and x2 to solve the cost minimization problem for the firm? Explain.

iii. If the firm’s factor demand functions for x1 and x2 are as follows:

   x1= p ^3/ (27 w1^2 w2)

   x2= p ^3/ (27 w1 w2^2)

a. How the optimal quantity of each input changes when price of input changes?

b. How the optimal quantity of one input changes when price of other input changes?

c. How the optimal quantity of each input changes when price of that input changes?

Alumni donations are an important source of revenue for college and universities. If administrators could determine the factors that could lead to increases in the percentage of alumni who make a donation, they might be able to implement policies that could lead to increased revenues. Research shows that students who are more satisfied with their contact with teachers are more likely to graduate. As a result, one might suspect that smaller class sizes and lower student-faculty ratios might lead to a higher percentage of satisfied graduates, which in turn might lead to increases in the percentage of alumni who make a donation. Table 15.13 shows data for 48 national universities (America’s Best Colleges, Year 2000 Edition). The column labeled Graduation Rate is the percentage of students who initially enrolled at the university and graduated. The column labeled % of Classes Under 20 shows the percentage of classes offered with fewer than 20 students. The column labeled Student-Faculty Ratio is the number of students enrolled divided by the total number of faculty. Finally, the column labeled alumni Giving Rate is the percentage of alumni that made a donation to the university.

Chi-Square Test of Goodness of Fit. FOR THIS AND THE NEXT PART. The historical market shares of 4 firms are shown below. Also shown is the number of customers who, in a recent survey, indicated which firm they patronize. Note that the total number of customers in the survey is 200.

2.       In order to test whether the market shares have changed - in light the recent survey results - the following null hypothesis is defined for each firm:

3.       H₀: p1 = 0.40, p2 = 0.32, p3 = 0.24, p4 = 0.04

4.       Calculate the chi-square statistic for this study. Note: to do this, you should first calculate the "expected number" of customers for each firm based on the historical market share and the surveyed number of 200 customers.

PART 2

1.       Chi-Square Test of Goodness of Fit. CONTINUING FROM THE PRECEDING. What is the critical value of the test statistic? What can we conclude from the result?

You are a manager at a retail pharmacy outlet called One Pharmacy. Your store is in a very socially and culturally diverse suburb. Sometimes your staff members complain that the customers they serve are rude, unreasonable or difficult to understand. You realise your customer service systems may need to be reviewed and updated to best support your staff in serving the needs of your customers

You are a manager at a retail pharmacy outlet called One Pharmacy. Your store is in a very socially and culturally diverse suburb. Sometimes your staff members complain that the customers they serve are rude, unreasonable or difficult to understand. You realise your customer service systems may need to be reviewed and updated to best support your staff in serving the needs of your customers

An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in minutes) differ between the three routes. He obtains the following data after traveling each route for one week.

a-1. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS", "p-value" to 4 decimal places and "F" to 3 decimal places.)

ANOVA
Source of Variation   SS   df   MS   F   p-value
Between Groups                  
Within Groups                  

a-2. At the 1% significance level, do the average commute times differ between the three routes. Assume that commute times are normally distributed.

• Yes since the p-value is less than significance level.
• No  since the p-value is less than significance level.
• No  since the p-value is not less than significance level.
• Yes  since the p-value is not less than significance level.

b. Use Tukey’s HSD method at the 1% significance level to determine which routes' average times differ. (You may find it useful to reference the q table). (If the exact value for n_T − c is not found in the table, use the average of corresponding upper & lower studentized range values. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Population Mean Difference   Confidence Interval   Do the average times differ?
μRoute 1 − μRoute 2 [       ,       ]  
μRoute 1 − μRoute 3 [       ,       ]  
μRoute 2 − μRoute 3 [       ,       ]  

What is the NPV of the project? Project life: 3 years Equipment: Cost: $18,000 Economic life: 3 years Salvage value: $4,000 Initial investment in net working capital: $2,000 Revenue: $13,000 in year 1, with a nominal growth rate of 5% per year Fixed cost: $3,000 in year 1 Variable cost: 30% of revenue Corporate tax rate (T): 40% WACC for the project: 10% This project does not create incidental effect.

1. An electronics company wants to compare the quality of their cell phones to the cell phones from three competitors. They sample 10 phones from each company and count the number of defects for each phone. If ANOVA was used to compare the average number of defects, then the treatments would be defined as:

Select one:

a. The three companies

b. The total number of phones

c. The number of cell phones sampled

d. The average number of defects

2. A grocery store chain wants to compare the amount of withdrawals that its customers make from automatic teller machines (ATMs) located within their stores. They sample 3 withdrawals from each of four different locations (12 withdrawals total) to compare the four treatment means. What is the critical value between the accept and reject regions if the level of significance is 0.05?

Select one:

a. 8.81

b. 9.55

c. 3.86

d. 19.16

e. 4.07

5. ABC Company is preparing their master budget and is preparing a schedule of expected cash collections from sales for the first quarter of 2019. They expect sales in January to be $400,000, February to be $300,000, and March to be $500,000. !0% of the sales will be paid for in cash. The remainder will be charged on account. From past experience, the company knows their customers take 3 months to pay their bills in total, with 40% of a month’s sales on account collected in the month of sale, another 50% collected in the month following sale, and the remaining 10% are collected in the second month following sale. All credit sales are collected. The amount of credit sales in October 2018 totaled $600,000, November 2018 totaled $700,000, and December 2018 totaled $800,000.

1. Prepare a schedule of expected cash collections from sales for only January and February 2019.

                                       January                                                         February

2. What is the expected accounts receivable balance on March 31, 2019?   $_________________

Show your work: