70.2K

Verified Solution

Link Copied!

QUESTION TWO

The following information was extracted from ABC Ltds financial statements for the year ended 31 December 2019.

1. Sales on 30 November 2019 were K100 million and K110 million on 31 December 2019. For the year 2020, sales are expected to double at a constant monthly rate.
2. 80% of the sales made are on account; the remainder on cash.
3. From past experience, 5% of the receivables have turned out to be irrecoverable.
4. Credit customers pay as follows:
   1. 75% in the month following the sale;
   2. 15% two months after the sale month.
5. Inventory levels are maintained at 20% of the following months sales.
6. Accounts payables are at settled at 30 days after purchase.

Required:

1. Prepare a collections schedule for the three-month period from January to March 2020.

[5 Marks]

2. Prepare a cash forecast for the three-month period from January to March 2020.

[5 Marks]

3. Assess the Operating Cycle ratios and their implication on the working capital requirements of the company for the forecast period.

[15 Marks]

QUESTION ONE A Consumer seeks to maximize a utility function U(x, y) subject to his income constraint given by: P1x + P2y = M. a) What is meant by a duality problem in constrained optimization? Please provide examples. [6 marks] b) Set up a Lagrange function for this optimization. [3 marks] c) State the First order conditions and explain how you would solve for the critical values. [6 marks] d) Explain the meaning of the Lagrange multiplier as it related to this optimization problem. [4 marks] 1 e) Given a utility function: U(x,y) = xzyz and an income constraint: 50 = 3x + 2y maximize the utility function, subject to the constraint. [6 marks] QUESTION ONE A Consumer seeks to maximize a utility function U(x, y) subject to his income constraint given by: P1x + P2y = M. a) What is meant by a duality problem in constrained optimization? Please provide examples. [6 marks] b) Set up a Lagrange function for this optimization. [3 marks] c) State the First order conditions and explain how you would solve for the critical values. [6 marks] d) Explain the meaning of the Lagrange multiplier as it related to this optimization problem. [4 marks] 1 e) Given a utility function: U(x,y) = xzyz and an income constraint: 50 = 3x + 2y maximize the utility function, subject to the constraint. [6 marks]

Answer & Explanation Solved by verified expert

See Answer