By Engler D. A.

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**Extra resources for A pseudolikelihood approach for simultaneous analysis of array comparative genomic hybridizations (2**

**Example text**

Regardless of the size of p a n d p , a n y level of X where MP is negative will always be irrational since a higher level of o u t p u t could be achieved with fewer inputs. T h e profit maximizing condition of equality between dT/dX a n d p jp is shown in Fig. 1. 9) is satisfied at point B. O p t i m a l i n p u t is O C , yielding o u t p u t of O D . Profit is p times O A since x y x x x x X x x x y y 7r=/> (OD)-/>,(OC) 7 =p (OD)-p,(AD) j =/>,(OA). O p e r a t i o n at a n y point other t h a n B would yield a smaller profit u n d e r the given price regime.

For fixed o u t p u t , m a x i m u m profit is specified by the intersection of the least-cost isocline with the a p p r o p r i a t e isoquant segment. For fixed outlay, it is the intersection of the least-cost isocline with the relevant iso-cost locus. T h e above analysis covers the situation where the total outlay limitation on the response process is known. e. by the o p p o r t u n i t y cost t h a t would occur if better profit possibilities elsewhere were foregone.

45). W i t h a p p r o p r i a t e a c c o m m o d a t i o n of a n y required b o u n d a r y solutions, simultaneous solution of each of these r sets (subject to the secondorder condition t h a t all MP be non-negative) gives the required r sets of least-cost i n p u t arrays. 47) subject to the constrained objective function: ^iP^-YLP^+HlPJ-R) (3-50) where R is the prespecified fixed level of total revenue ^p T . Setting dnjdX a n d dnjdX equal to zero, we have the rn+ 1 conditions: h ih p„{dr ldX ) -Pi+fytfrjdX^O, k t R-lP„r =o.