Value Rite Inc. is a centralized processor of promotional manufacturers’ coupons for firms in the food products industry. Its sophisticated records division monitors promotional sales data in order to highlight effective promotions and limit coupon fraud. A production function for the records division is estimated as follows:
X = 4S + 100ST + 2T
Where X is the number of coupons (in thousand units), S the amount of computer staff input (in worker weeks) and T the amount of computer time input (in machine weeks). A computer staff earns $400 per week while a machine costs $200 per week. Total expense for the records division is limited to $100,000 per week.
1. Using the method of Lagrangean Multiplier, compute the optimal levels of S, T and X if the objective of the records division is to process as many coupons as possible.
2. Using the value of the Lagrangean multiplier, decide the marginal cost of processing additional coupons. Describe your calculations.