quantitative finance

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Question 41316


Quantitative Finance

Highland Co. is a manufacturing firm. The company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 100 units of A per day. Both products use one raw material, of which the maximum daily availability is 240 lb. The usage rates of the raw material are 2 Ib per unit of A, and 4 lb per unit of B. The profit units for A and B are £20 and £50 respectively.

a) Formulate a linear programming model for this problem.

b) Use the graphical method to find the optimal solution to the following Linear Program.

Explain the effect(s) of changing constraint x_1+x_2<30 to x_1+x_2<31 in the above linear program (i.e., part b).[

The manager of the Highland Co. (the above company) wishes to forecast the sales volume of product A in the next period. The company has accumulated the following sales data for the past 10 periods.

e) Compute the last value forecast, a four period moving average and an exponential smoothing forecast (a = 0.3) for the above sales data. In each case, estimate the sales volume of product A in period 11.

f)Compute the Mean Absolute Errors (MAE) for the results in part (e), and comment on the accuracy of the sales forecast pertaining to each of the three techniques. Explain if selecting a larger value of a would have any effect on the performance of the exponential smoothing method in this case and why.[10% of marks]

g) Discuss how the Business Analytics methods could be useful to decision makers inAmazon.

Question 37326


Quantitative Finance

KaYa Ltd manufactures furniture. The information below relates to a 1970's retro bookshelf that they make for boutique buyers. They have a medium sized factory, and the information below only relates to the production run making the bookcases. The production manager Jess,decided to run three separate production runs of bookcases during July-December 2021.There are two manufacturing overhead allocation rates that are assigned to production. One is using the cost-driver of labour-hours and the other uses kilowatts of electricity used in a production run.

Manufacturing overhead costs in January-June 2021 were budgeted to be $102,250. The actual manufacturing overhead was $105,500. Allocated during that time was $108,250 of manufacturing overhead.

For July - December 2021 it was estimated that manufacturing overhead per production run would total $7,360, there would be 50 labour hours per production run and that 15 machine hours would be used in each production run. Jess has budgeted that each time a machine runs for an hour it uses 100 kilowatts of electricity. The cost pool of total overhead is split between the two cost drivers equally. The staff that work on the production run are paid $20 per hour,and each book case uses $35 of wood.

a) In January to June 2021, how much overhead was over or under-applied? What may have caused this?

b) State at least three overhead costs that could be included in each overhead application rate cost pool. Explain if this would be a fixed or a variable cost and why it would be included in the electricity or labour cost pool.

c) Calculate the predetermined overhead application rates for a single production run that would be used for absorption costing purposes during June 30-December 312021. Round your allocation rate to 2 decimal points.

d) In production run 1,75 bookcases were made. In this production run 48 labour hours were used, and the machines ran for a total of 13 hours. What is the cost per bookcase? Show all workings.

e) At the end of December, 12 bookcases from production run 1 were in ending inventory. There had been no opening inventory. Calculate the cost of the finished goods (on the balance sheet) and the Cost of Goods Sold (on the income Statement)for production run 1.(A morka)

f) What would you recommend that we sell each bookcase for? Show your calculations.

Question 37325


Quantitative Finance

Three companies have provided you with information regarding April data. The data isincomplete. Complete the table below with all relevant information about all threecompanies.

a) In May, DyOw Lt'd sales volume stayed the same, InSh Ltd's sales volume increasedby 20% and KiBr Ltd's sales volume decreased by 5 units. Prepare the contributionmargin statement for each company in May.

b) Which of the above three companies do you think is in the best financial position andwhy. Include in your answer a discussion of the margin of safety, and offer someadvice to each manager.

c) Describe how linearity and the relevant range may impact upon decision making inthese firms for July.

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