The Hindu Business Line : LP model in a paint company

FENTON Paints Ltd manufactures three grades of paints — Venus, Diana and Aurota. The plant operates on a three-shift basis and the data presented in Table 1 are made available from the production records.

There are no limitations on other resources. The particulars of sale forecasts and estimated contribution to overheads and profits are given in Table 2.

Due to commitments already made, a minimum of 200 kilolitres per month of Aurota has to be necessarily supplied the next year. Just as the company was able to finalise the monthly production programme for the next 12 months, an offer was received from a nearby competitor for hiring 50 machine shifts per month of milling capacity for grinding Diana paint, that can be spared for at least a year.

However, due to additional handling and the profit margin of the competitor involved, by using this facility, the contribution from Diana will get reduced by Rs 1.50 per litre.

Formulate this problem as a linear programming (LP) model for determining the monthly production programme to maximise contribution. You are not required to solve the LP model.

Let x litres of Venus grade paint, y litres of Diana grade paint and

z litres of Aurota grade paint be manufactured as shown in Table 3.

Maximisation of contribution:

Maximise z = 4x + (3.6 - 1.5)y + 2.5z

z = 4x + 2.1y + 2.5z

Subject to constraints

Special additive: 0.30 x + 0.25 y + 0.75 z less than or equal to 6,50,000

Milling x/2500 + y/ 3500 + z/5000 less than or equal to 110 - 55

x/2500 x 35000 + y/3500 x 35000 + z/5000 x 35000 less than or equal to 55 x 35,000

14x + 10 y + 7z less than or equal to 19,25,000

Packing: x/12000 + y/12000 + z/12000 less than or equal to 100

x + y + z =100 x 12,000 = 12,00,000

0.30x + 0.25y + 0.75z less than or equal to 6,50,000

14x +10y + 7z less than or equal to 19,25,000

x + y + z less than or equal to 12,00,000

Subject to x being less than or equal to 1,20,000

Y being less than or equal to 4,50,000

2,00,000 being less than or equal to and z being less than or equal to 6,00,000. (2,00,000 is prior commitment)

Right option

IF THE profit-volume (PV) ratio is 40 per cent and sales value Rs 10,000, the variable cost will be: a) Rs 4,000; b) Rs 6,000; c) Rs 5,000; d) none of the above.

Variable cost ratio is a complement of PV ratio. When PV ratio is 40 per cent, variable cost ratio is 60 per cent of sales. Sixty per cent of Rs 10,000 will be Rs 6,000. Hence option (b) is correct.

In a service department manned by one server, on an average one customer arrives every five minutes, the service time is four minutes per customer. The probability of the server being idle is: a) 40 per cent; b) 20 per cent; c) 15 per cent; d) none of the above.

S = 60/4 = 15 per hour.

R = 12/15, that is, 4/5

A = 60/5 =12 per hour.

The probability of server being idle is 1 - R, that is, 1 - 4/5 = 1/5, that is, 20 per cent. Hence, option (b) is correct.

A company budgets for fixed overhead of Rs 24,000 and production of 4,800 units. Actual production is 4,200 units and fixed overhead cost incurred is Rs 22,000. The fixed overhead volume variance is: a) Rs 3,000 (adverse); Rs 1,000 (adverse); Rs 2,000 (favourable); Rs 3,000(favourable)

SR = BFO/BQ, that is, Rs 24,000 / 4,800 units = Rs 5 per unit.

Fixed overhead volume variance = SR (AQ - BQ)

5 (4200 - 4800) = Rs 3000 A. Hence, option (a) is correct.

Flexible budgeting

VIKAS Textiles Ltd has just completed the first year of operation on March 31, 2003, and the summarised result of the operating as as follows:

Installed capacity: 20,000 kg of yarn

Production and sales: 14,000 kg of yarn

The income and expenditure details are given in Table 4.

i) The managing director wishes to expand the operation for the year 2003-04 and has asked you to prepare Flexible Budgets on capacity utilisation levels of 80 per cent, 90 per cent and 100 per cent based on the following estimate:

a) Price (Rs/kg of yarn) at 80 per cent level — Rs 210; at 90 per cent level — Rs 200; at 100 per cent — Rs 195

Whatever produced during the year is expected to be sold within the year.

b) Increase in variable cost components: materials at12 per cent; labour at 10 per cent; factory overheads at 15 per cent; and marketing overheads at 20 per cent.

c) Inflation rate applicable to fixed cost is 15 per cent. Additionally, if the capacity utilisation exceeds 80 per cent, fixed cost is expected to increase by 10 per cent up to 100 per cent capacity utilisation.

Comment on this plan of sub-contracting with a view to maximising the profit of the company.

The flexible budget (100 per cent capacity 20,000 kg) is shown in Table 5.

Sub-contracting:

Cost (4,000 x 105) = Rs 4,20,000

Variable cost (mfg) 4,000 x 102 = Rs 4,08,000

Incremental cost on sub-contracting — Rs 12,000

Increase in fixed cost saved — Rs 1,12,700

Net saving — Rs 1,00,700

The profit is worked out in Table 6.

The production manager's plan of sub-contracting the production of 4,000 kg will result into the incremental profit of Rs 1,00,700. Then the profit of the company will maximise at Rs 7,21,000.

The working note is presented in Table 7.

Queue system

A FOOD storage agency receives stocks of foodgrains at an average rate of eight trucks per hour. A crew of three operatives can unload on an average 10 trucks per hour.

Operatives are paid a wage rate of Rs 20 per hour. If the crew size is doubled, the unloading rate can be increased to 18 trucks per hour.

When a truck is kept waiting idle an hourly demurrage charge at the rate of Rs 60 has to be paid.

Determine whether it would be worthwhile to employ a second crew. You may assume that the conditions of a (M/M/1) queue system as applicable.

Arrival rate (lambda) = 8 per hour

Service rate (mu)= 10 per hour

Present cost of unloading [for three operatives] = 3 x 20 per hour = Rs 60 per hour.

Traffic intensity = P = lambda/mu = 8/10 = 0.80

Average queue length = P2/1 - P = (0.80){+2} = 0.80 x 0.80 / 1 - 0.800.20 = 3.2

Opportunity cost per unit time = 60 x 3.2 = Rs 192

Actual cost of current year = 60 x 3.2 = Rs 192

Total cost of current year = opportunity cost + actual cost = 192 + 192 = Rs 384

Proposal: If crew is doubled, service rate = mu = 18 per hour

Cost of unloading [for six operatives] = 6 x 20 = Rs 120 per hour

Traffic intensity = P lambda/mu = 8/18 = 4/9 = 0.44

Average queue length = P2/1-P = (0.44){+2} /1-0.44 = 0.44 x 0.44/0.56 = 0.35

Opportunity cost = 60 x 0.35 = Rs 21

Actual cost = 120 x 0.35 = Rs 42

Total cost = 21 + 42 = Rs 63

Thus the total cost of by employing second crew is less than the single crew. Hence, it is worthwhile employing the second crew.

Note: Decision to employ second crew will not change even if we consider total salary for crew is taken as Rs 20 per hour.

Simulation

SHREE Lakshmi Finance Corporation is an investment company.

The management of the company wants to study the investment in a project based on the following three factors: a) market demand, b) profitability, and

c) amount of investment required.

In analysing a new consumer product, the corporation estimates the probability distribution shown in Table 8.

The following random numbers are to be used:

a) For demand: 28, 57, 60, 17, 64, 20, 27, 58, 61, 30.

b) For profit: 19, 07, 90, 02, 57, 28, 29, 83, 58, 41.

c) For investment: 18, 67, 16, 71, 43, 68, 47, 24, 19, 97.

Required: Using simulation technique, repeat the trial ten times, compute the return on investment for each trial considering these three factors into account. Approximately,what is the highest likely return?

The annual demand, profit per unit and investment required are presented in Tables 9, 10, and 11 respectively. And from Table 12 it can be said that the highest return is Rs 3,15,000 on the sale of 35,000 units.

(To be continued)

(Suggested answers to the December 2003 ICWA (Stage II) paper on management accounting.)

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