Your company has been asked to quote for a new product. Although you were not involved in the manufacture of the prototypes, similar products have been made by the existing labour force and machinery.

The production records for two similar products, K and L, have been examined and the direct labour cost is summarised below:

Cost of Product Product unit K L

$ $

First 250 520 Second 200 380 3 and 4 360 760 5, 6, 7 and 8 648 1280 9-16 (incl.) 1166 2400 It has been estimated that the direct labour cost of the first unit of the new product will cost $400.
Regression analysis must be employed.
Formulate which may be useful include:
Y = aX-b where Y = Cumulative average cost a = Cost of first unit X= Cumulative units completed b = Learning rate and, in the standard regression equation y = a+bx (I:y) (I:x2)- (I:x) (I:xy)
a=-n -(I:-x2-) _- (I-:x-) 2- -
b = n (I:xy) - (:Ex) (I:y)
n (I:x2) - (:Ex) 2 Based on the information given above, the learning rate for product K is 0·1522.
REQUIRED ~a) Determine the relationship between the cumulative no. of units completed and the cumulative average direct labour cost for product L

(b) Estimate a relationship for the new product

(c) Using this relationship, estimate the direct labour cost for a subsequent quantity of 7, i.e. units 2-
8 (inclusive) of the new product.
ICMA. PS, Part I, Quantitative Techniques, November 1979.