Checking the Assume Non-Negative box ensures that Solver considers only combinations of changing cells in which each changing cell assumes a non-negative value. We checked the Assume Linear Model box because the product mix problem is a special type of Solver problem called a linear model. Essentially, a Solver model is linear under the following conditions:
Therefore, the labor constraint is evaluated by adding together the terms of the form (changing cell)*(constant) and comparing the sums to a constant. Both the labor constraint and the raw material constraint satisfy the linear model requirement.
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Each demand constraint also satisfies the linear model requirement, because each is evaluated by adding together the terms of the form (changing cell)*(constant) and comparing the sums to a constant.
If a Solver model is linear and we select Assume Linear Model, Solver is guaranteed to find the optimal solution to the Solver model. If a Solver model is not linear, Solver may or may not find the optimal solution.
After clicking OK in the Solver Options dialog box, we return to the main Solver dialog box, shown earlier in Figure 27-7. When we click Solve, Solver calculates an optimal solution (if one exists) for our product mix model. As I stated in Chapter 26, an optimal solution to the product mix model would be a set of changing cell values (pounds produced of each drug) that maximizes profit over the set of all feasible solutions. Again, a feasible solution is a set of changing cell values satisfying all constraints. The changing cell values shown in Figure 27-9 are a feasible solution because all production levels are non-negative, production levels do not exceed demand, and resource usage does not exceed available resources.
The error message and screenshot clearly indicate Model.Category is null. This means the action does not populate the Category property before passing the model to the view. The two DataMgmt actions shared above do not populate a model and I assume that's the problem. You'll need to review your design as it looks like your expectations do not match how the code works.
In addition to direct assessments of timed administration of nutrients, other studies have explored questions that center upon the pattern of when certain protein-containing meals are consumed. Paddon-Jones et al. [97] reported a correlation between acute stimulation of MPS via protein consumption and chronic changes in muscle mass. In this study, participants were given an EAA supplement three times a day for 28 days. Results indicated that acute stimulation of MPS provided by the supplement on day 1 resulted in a net gain of 7.5 g of muscle over a 24-h period [97]. When extrapolated over the entire 28-day study, the predicted change in muscle mass corresponded to the actual change in muscle mass (210 g) measured by dual-energy x-ray absorptiometry (DEXA) [97]. While these findings are important, it is vital to highlight that this study incorporated a bed rest model with no acute exercise stimulus while other work by Mitchell et al. [125] reported a lack of correlation between measures of acute MPS and the accretion of skeletal muscle mass.
Based on this research, scientists have also attempted to determine which of the EAAs are primarily responsible for modulating protein balance. The three branched-chain amino acids (BCAAs), leucine, isoleucine, and valine are unique among the EAAs for their roles in protein metabolism [150], neural function [151,152,153], and blood glucose and insulin regulation [154]. Additionally, enzymes responsible for the degradation of BCAAs operate in a rate-limiting fashion and are found in low levels in splanchnic tissues [155]. Thus, orally ingested BCAAs appear rapidly in the bloodstream and expose muscle to high concentrations ultimately making them key components of skeletal MPS [156]. Furthermore, Wilson and colleagues [157] have recently demonstrated, in an animal model, that leucine ingestion (alone and with carbohydrate) consumed between meals (135 min post-consumption) extends protein synthesis by increasing the energy status of the muscle fiber. Multiple human studies have supported the contention that leucine drives protein synthesis [158, 159]. Moreover, this response may occur in a dose-dependent fashion, plateauing at approximately two g at rest [31, 157], and increasing up to 3.5 g when ingestion occurs after completion of a 60-min bout of moderate intensity cycling [159]. However, it is important to realize that the duration of protein synthesis after resistance exercise appears to be limited by both the signal (leucine concentrations), ATP status, as well as the availability of substrate (i.e., additional EAAs found in a whole protein source) [160]. As such, increasing leucine concentration may stimulate increases in muscle protein, but a higher total dose of all EAAs (as free form amino acids or intact protein sources) seems to be most suited for sustaining the increased rates of MPS [160].
It is well known that exercise improves net muscle protein balance and in the absence of protein feeding, this balance becomes more negative. When combined with protein feeding, net muscle protein balance after exercise becomes positive [161]. Norton and Layman [150] proposed that consumption of leucine, could turn a negative protein balance to a positive balance following an intense exercise bout by prolonging the MPS response to feeding. In support, the ingestion of a protein or essential amino acid complex that contains sufficient amounts of leucine has been shown to shift protein balance to a net positive state after intense exercise training [46, 150]. Even though leucine has been demonstrated to independently stimulate protein synthesis, it is important to recognize that supplementation should not be with just leucine alone. For instance, Wilson et al. [139] demonstrated in an animal model that leucine consumption resulted in a lower duration of protein synthesis compared to a whole meal. In summary, athletes should focus on consuming adequate leucine content in each of their meals through selection of high-quality protein sources [139]. 2ff7e9595c
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