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Here is a question that I have no clue to work on:
15 Bridon
The following costs per unit relate to the production and sale of 20,000 of a product by Bridon Company, for the financial year that has just ended:
$ per unit
Direct material 30
Direct labour 10
Overheads:
Variable 10
Fixed 10
total cost 60It has been estimated that major cost increases will apply to the following year, assuming that production and sales volumes are still 20,000 units.
Increase
Direct material 20%
Direct labour 5%
Variable overhead 5%
Fixed overhead 10%
It would be possible to substitute a cheaper grade of direct material, allowing the
cost of direct materials to be $31.25 per unit. However, a rejection rate of 5% will arise.(There are currently no rejected units.) This would require an additional annual inspection cost of $30,000. In the past, the selling price has been set using a mark-up of 50% on full cost and a price of $90 per unit was charged in the current year. However, the sales manager has estimated the price/demand relationships as follows:Price $80 $84 $88 $90 $92 $96 $100
Demand (000s units) 25 23 21 20 19 17 1 5Required
(a) Decide whether the product should use the regular or the cheaper grade of material.
(b) Calculate the price that should be charged for the product to maximise the annual profit, and the profit that should be expected.I have no clue at all, so please advise how to do part (a) and part (b). I just can’t seem to find the MR equation in the question.
Also, in the final F5 exam, can we be asked about linear porgramming dealing with minimization or only maximization is assessed?
Thanks.
For part (a), the price of the existing material will increase to 30 + 20% = $36 per unit – you can apply the rates of inflation to the other costs and work out the current cost per unit. (It comes to $68 per unit I think)
The other material will cost $31.25 per unit, but because of the rejection rate it will mean that for every 95 ‘good’ units we produce we will have to make 100 units.
The cost of making one unit will be 31.25 (for the material) plus the other costs as before (with inflation) plus an extra 1.50 per unit for extra inspection (30000/20000). I think that this comes to $64.75 per unit (but check my arithmetic 🙂 )
However this is the cost of producing one unit, but because 5% are rejected, it means we have to make 100 units to end up with 95 good units. So the cost of each good unit = 64.75 x 100/95 = $68.16.
This is greater than the cost of using existing material so better to stay the with the regular material (but check my arithmetic!)For part (b) you can see from the price/demand figures that for every $4 increase in selling price, the demand falls by 2000 units.
So you can use the formulae on the formula sheet to get a and b for the price demand equation, and then put the same values for a and b in the marginal revenue equation.Finally, yes – you can be asked to do minimisation of costs or maximisation of profits in linear programming questions.
for part (a) I had done exactly the same thing you had done but I got surprised when I read the suggested answer in the Emile woolf book:
(a) Budgeted variable production costs
Cost in current year Inflation Cost next year
Current material
New material
$ %
Direct material 30 20 36.0 31.25
Direct labour 10 5 10.5 10.50
Variable o’hd 10 5 10.5 10.50
50 57.0 52.25
Cost of rejected units (5%) 2.75
55.00
Using the cheaper substitute material will reduce the variable unit cost by $2, but fixed costs will increase by $30,000. Since annual sales at the current price will be 20,000 units, it will be more profitable to use the cheaper material.
The unit variable cost will be $55.So this answer is incorrect yes?
The way that they have worded the question, I think that their answer is incorrect.
Had it been that the material was rejected, then OK, but the question says that units are rejected.
This was not a real exam question. If it had been then I am confident that mine would have been the correct answer (or else they would have changed the wording of the question)!
🙂
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