The Katto Co. is considering its production plan for the next month for two products, X and Y. B'lth products use some of the firm's manufacturing and bottling capacity which would otherwise be unused. The forecast contributions per unit of X and Y for sales up to 1000 units each are £1.50 and £2.00 respectively. The production requirements of X and Y and the capacity of the relevant manufacturing and bottling plant is as follows:

Plant Hours required per unit Total capacity Manufacturing Bottling X

3 6

y 5

2 Hours 1500 1000 Product Y requires special quality control and a maximum production limit of 270 unit ofY has been established by the company's manager.

(a) Calculate the production plan for quantities of X and Y for the next month which maximises the contribution from the products. What is the contribution?

(b) The company is considering sub-contracting the bottling of X and Y. What is the maximum the company should be prepared to pay for an additional (i) I hour,

(ii) 10 hours, (iii) 100 hours of bottling capacity? Explain the differences, if any, between the hourly prices.

(c) The company is considering increasing the price ofY by £0.25 per unit, and it expects that the maximum sales will fall to about 700 units. Should the proposal be accepted, and if so what amount of X and Y should be produced next month?