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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).