Download Model answer P2: optimum production plans Assume that it

Model answer P2: optimum production plans
Assume that it is one year later, but that the restriction on the
specialist material still exists, that is, only 28,000 kilograms are
available for the year.
All other information is as previously stated with the exception of the
following:
• Scarsprey Co has rebranded the super kettle as a premium
product and has increased the price so that it yields a
contribution of $34 per unit. However, this means that the
maximum demand for super kettles is 2000 units a year.
In summary:
Maximum market demand
(kettles a year)
Contribution / kettle ($)
Material / kettle (kgs)
basic
deluxe super
4500
8
2
2000
15
5
2000
34
8
• The sales director has also already accepted an order for 800
deluxe kettles which, if not supplied in total, would incur the
same financial penalty as before, that is $2000. This quantity of
kettles is included in the maximum market demand figure
above.
You can also continue to assume that, as Scarsprey operates just in
time production methods, opening and closing inventory levels are
zero.
Questions
1. Formulate Scarsprey’s optimum production plan for the ‘new’
year, including an evaluation of whether it is financially
worthwhile for the company to break the contract.
2. State the shadow price of a kilogram of the specialist material
and calculate the quantity of kilograms of material over which
this shadow price applies.
Solution
1. Once again, initially look at the situation where the company fulfils
the contract.
basic
4.00
2nd
Contribution / kg ($)
Ranking
deluxe super
3.00
4.25
rd
3
1st
Firstly, make the 800 deluxe kettles required for the contract, before
using the rest of the material resource to make super kettles, and
then basic kettles. (Note that the order of priority for making the basic
and super kettles has reversed). If there is any material left we can
make more deluxe kettles.
basic
Minimum
units
to
satisfy
contract
Material required for contract
(kgs)
Number of units to satisfy
maximum demand (super) or
use of remaining resources
4,000
(basic)
Material used for production of
basic and super (kgs)
8,000
Material available and used
Total number of kettles to be
produced
4,000
deluxe super
Total
800
4,000
4,000
0
2,000
0
16,000 24,000
28,000
800
2,000
The contribution resulting from this production (and sales) plan is:
basic
deluxe
super
(4,000 x $8)
(800 x $15)
(2,000 x $34)
$
32,000
12,000
68,000
112,000
Now consider the impact of breaking the contract, and whether it is
financially worthwhile.
Simply ignore the requirement for a minimum of 800 deluxe kettles
and, using fundamental principles, reformulate the production plan,
that is:
basic
Number of units to satisfy
maximum demand (basic) or
use resources (super)
4,500
Material used for production of
basic and super (kgs)
9,000
Material available and used
Total number of units to be
produced
4,500
deluxe super
Total
600
2,000
3,000
16,000 28,000
28,000
600
2,000
The contribution resulting from this revised production (and sales)
plan is:
basic
deluxe
super
(4,500 x $8)
(600 x $15)
(2,000 x $34)
$
36,000
9,000
68,000
113,000
In other words, there is a rise in contribution of $1,000.
What’s happened is that by making 200 fewer deluxe kettles, we
release 1,000 kgs (200 x 5 kgs). These kettles were yielding a
contribution of (200 x $15) $3,000, which is now sacrificed to make
way for alternative production ($3,000 could be described as the
opportunity cost).
Instead, we can use 1,000 kgs to make 500 more basic kettles (1,000
kgs / 2 kgs per unit). These 500 basic kettles will yield contribution of
(500 x $8) $4,000, the same rise of $1,000 calculated above.
Alternatively, the rate at which contribution was earned on deluxe
kettles was $3 per kg, but is $4 per kg on the basic. Therefore, the
1,000 scarce kilograms are now earning $1 more per kilogram, an
increase in contribution of $1,000.
Whichever way you look at it, the new production plan increases
contribution by only $1,000, which is less than the financial penalty
for breaking the contract of $2,000 (remember that the contract was
for supplying 800 deluxe kettles in total, and this has not been done).
Therefore, in simple financial terms, unless the rise in contribution is
in excess of $2,000, then it is not financially worthwhile to renege on
the contract, even before consideration of the non financial factors.
The optimum production plan is to make 4,000 basic kettles, 800
deluxe kettles and 2,000 super kettles.
2. Should Scarsprey be able to source additional material from
elsewhere, then clearly it will do so as long as the premium for
each kilogram is less than $4. Since the contribution per kilogram
of material used in producing the basic kettle is $4, this would
make it worthwhile to source material from the alternative supplier.
This $4 is therefore the shadow price of a kilogram of material, but
will only stay at $4 per kilogram as long as the material is being used
to make basic kettles, that is, up to the maximum demand of 4,500
units - in other words, for another 1,000 kgs (500 units x 2 kgs).