Limiting Factors

Horngren Co
Horngren Co manufactures a range of dairy products. It produces three types of yoghurt which it sells in 2 kg tubs to hotels and holiday resorts.

Details of demand, costs and selling prices for the three types of yoghurt are as follows:

Product Natural Fruity Luxury
Maximum demand per month (units) 5,000 10,000 15,000
$ per unit $ per unit $ per unit
Selling price 15 22 30
Direct labour 4 8 12
Direct material 3 3.75 4.50
Fixed production overhead 1 4 6
Notes:

Direct labour is paid at a rate of $8.00 per hour
Direct material costs are $1.50 per kg
The fixed production overhead is absorbed using a machine hours basis at a rate of $1 per hour. Fixed production overheads are a joint cost of the three products
An external supplier has offered to supply units of Natural, Fruity and Luxury for $11, $17 and $25 per unit respectively.

Horngren Co predicts the following availability of resources over the next three months:

Direct labour Direct material Machine capacity
Month 1 36,000 hours 75,000 kg 140,000 hours
Month 2 unlimited unlimited 120,000 hours
Month 3 27,000 hours unlimited unlimited
Direct material and the products made are perishable and thus no inventory is held.

Question
2. In Month 2 how many units of Fruity should Horngren Co buy from the external supplier assuming the company wants to maximise profit?

> Sir, i did not understand why did they approach the answer this way?
why have they considered the costs saved and not the contribution per unit of limiting factors to rank and decide the number of units of each product? 🙁

This is the explaination provided :

The correct answer is
3750
units.

In month 2 the limiting factor is machine capacity. Calculate the ranking of the products based on the cost saved by making per unit of limiting factor.

Product Natural Fruity Luxury
Buy in cost ($) 11 17 25
Variable cost of making ($) 7 11.75 16.50
Cost saved by making ($) 4 5.25 8.50
Machine hours per unit 1 4 6
Cost saved per machine hour 4 1.3125 1.416
Rank 1st 3rd 2nd
This shows that the products should be made in the order of Natural, Luxury then Fruity.

Machine hours available 120,000
Make 5,000 units of Natural (use 5,000 × 1) 5,000
Make 15,000 units of Luxury (use 15,000 × 6) 90,000
Remaining hours available for Fruity 25,000
The remaining hours are enough to make (25,000/4) = 6,250 units. Therefore, buy in (10,000 ? 6,250) = 3,750 units.

> however , i still dont get it ? how do we approach these type of questions ?