Advanced: Optimal production programme, shadow prices and relevant costs for pricing decisions Rosehip has spare capacity in two of its manufacturing departments

- Department 4 and Department 5. A five day week of 40 hours is worked but there is only enough internal work for three days per week so that two days per week (16 hours) could be available in each department. In recent months Rosehip has sold this time to another manufacturer but there is some concern about the profitability of this work.

The accountant has prepared a table giving the hourly operating costs in each department. The summarized figures are as follows

The labour force is paid on a time basis and there is no change in the weekly wage bill whether or not the plant is working at full capacity. The overhead figures are taken from the firm's current overhead absorption rates. These rates are designed to absorb all budgeted overhead (fixed and variable) when the departments are operating at 90% of full capacity (assume a 50 week year). The budgeted fixed overhead attributed to Department 4 is £36000 p.a.
and that for Department 5 is £50400 p.a.
As a short term expedient the company has been selling processing time to another manufacturer who has been paying £70 per hour for time in either department. This customer is very willing to continue this arrangement and to purchase any spare time available but Rosehip is considering the introduction of a new product on a minor scale to absorb the spare capacity.
Each unit of the new product would require 45 minutes in Department 4 and 20 minutes in Department 5. The variable cost of the required input material is £10 per unit. It is considered that:
with a selling price of £100 the demand would be 1500 units p.a.:
with a selling price of £110 the demand would be 1000 units p.a.; and with a selling price of £120 the demand would be 500 units p.a.

(a) You are required to calculate the best weekly programme for the slack time in the two manufacturing departments, to determine the best price to charge for the new product and to quantify the weekly gain that this programme and this price should yield. (12 marks)

(b) Assume that the new product has been introduced successfully but that the demand for the established mam products has now increased so that all available time could now be absorbed by Rosehip's main-line products. An optimal production plan for the main products has been obtained by linear programming and the optimal L.P.
tableau shows a shadow price of £76 per hour in Department 4 and of £27 per hour in Department 5. The new product was not considered in this exercise. Discuss the viability of the new product under the new circumstances. (5 marks)

(c) Comment on the relationship between shadow prices and opportunity costs.

Transcribed Image Text:

Department 4 () Department 5 () Power costs 40 60 Labour costs 40 20 Overhead costs 40 40 120 120