We have talked about the many qualities of whey that make it a preferred source of protein to consume after exercise such as its high content of essential amino acids (particularly leucine) and rapid absorption rate.
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  One question that has not received as much attention is how much whey delivers an optimal effect. Only one study has determined the dose response effect of protein provided after resistance exercise. That study was conducted in young healthy adults and showed that muscle protein synthesis reached a plateau with 20 grams of protein. The protein used in that study was egg. When 40 grams was ingested there was no further increase in muscle protein synthesis but there was an increase in protein oxidation.

To follow up on this study researchers performed a dose response study of whey protein provided after a bout of single leg knee extensions so that the rested leg could serve as a control. Subjects were older with an average age of 70 years.  After exercise they consumed a drink containing 0, 10, 20 or 40 grams of whey protein isolate. Measures of muscle protein synthesis were determined for 4 hours after exercise in the non-exercised leg (to assess the effects of simply ingesting whey without exercise) and in the exercised leg (to assess the effects of whey plus resistance exercise). Rates of muscle protein synthesis were higher in the exercised leg compared to the non-exercised leg at all doses of whey, consistent with the synergistic effect of whey and exercise.  In the non-exercised leg, there was a significant increase in muscle protein synthesis with the 20 gram dose but no further increase with 40 grams.  In the exercised leg, there was a significant increase in muscle protein synthesis with 20 grams of whey, and a further 32% increase with the 40 gram dose.  Leucine oxidation increased in a step wise manner in both legs as the dose of whey increased.  These data indicate that 20 grams of whey was necessary to significantly increase muscle protein synthesis at rest in elderly subjects and that increasing the dose to 40 grams did not amplify this effect.  After resistance exercise 20 grams whey is effective but an even greater effect can be achieved with 40 grams.  In summary these findings support the general conclusion that at least 20-40 grams of whey be consumed after exercise to achieve a maximal increase in muscle protein synthesis in older adults. 
Yang Y, Breen L, Burd NA, Hector AJ, Churchward-Venne TA, Josse AR, Tarnopolsky MA, Phillips SM. Resistance exercise enhances myofibrillar protein synthesis with graded intakes of whey protein in older men. Br J Nutr. 2012 Feb 7:1-9.