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A firm wants to minimize sum of discounted total cost of satisfying demands for a single input.
Then, taking into account discounting of cost and (1), there exists (nin mathbb {N} ) such that the sum of discounted total cost of satisfying demands in periods 1,…,t n+1−1 (where t n+1 is the period in which iteration n+1 starts under s ∗) under s is lower than under s ∗.
Thus, when we start the iteration n+1 in period t n+1, values of ( alpha _{j}^{ast }) and (q_{j}^{ast }) for j∈{t n,…,t n+1−1} computed in iteration n minimize the sum of discounted total cost of satisfying demands in periods j=t n,…,t n+1−1.
Since this holds also for all previous iterations, for each (nin mathbb {N} ), values (alpha _{j}^{ast }) and (q_{j}^{ast }) for j∈{1,…,t n+1−1} computed in iterations 1,…,n, minimize the sum of discounted total cost of satisfying demands in periods j=1,…,t n+1−1.
The last time they tried this, via legislation they sponsored in Sacramento, a Court of Appeal blew the whistle: "The premiums for policyholders who, because of their characteristics do not qualify for a particular discount must be surcharged in an amount equal to the total of the discounts given to the policyholders that qualified for the discount" (italics added).
That makes for a total of 16,400 discounted tickets for the season, and a price tag of about $1 million in (potentially) lost revenue.
The non-health GDP loss due to deaths of under-fives in ith country (NHGDPLoss) is the product of the total number of discounted life years above the minimum employment age lost, per capita non-health GDP in purchasing power parity (PPP) and total child deaths.
In symbolic terms, CPM for ith age bracket can simply be expressed as: ; is the number of diabetes associated deaths within ith age bracket for nth group of countries; DPYL i is the total number of discounted productive life years lost among persons of ith age bracket; and GNIPC n is the annual gross national income per capita in PPP.
Etsy expects its customers to receive a total average discount of $2,000. .
Since these shares cannot readily be sold outside the family, they are discounted for both lack of marketability and lack of control (typically a total discount of about 35percentt).
"PS, Esquire will be boasting of a large increase (still nearly three times fewer copies than us!) – you shouldn't believe it as over 50% of their January newsstand was sold in discount packs with incongruous titles like She and over 25% of the total were discount copies".
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com