Vollmer manufacturing makes three components for sale to refrigeration companies. the components are processed on two machines: a shaper and a grinder. the times (in minutes) required on each machine are as follows:

machine
component shaper grinder
1 6 4
2 4 5
3 4 2

the shaper is available for 120 hours, and the grinder for 110 hours. no more than 200 units of component 3 can be sold, but up to 1,000 units of each of the other components can be sold. in fact, the company already has orders for 600 units of component 1 that must be satisfied. the profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. write the lp model to maximize profit and solve it to find the optimal number of components and total profit.

Reliability and validity reliability and validity are two important considerations that must be made with any type of data collection. reliability refers to the ability to consistently produce a given result. in the context of psychological research, this would mean that any instruments or tools used to collect data do so in consistent, reproducible ways. unfortunately, being consistent in measurement does not necessarily mean that you have measured something correctly. to illustrate this concept, consider a kitchen scale that would be used to measure the weight of cereal that you eat in the morning. if the scale is not properly calibrated, it may consistently under- or overestimate the amount of cereal that’s being measured. while the scale is highly reliable in producing consistent results (e.g., the same amount of cereal poured onto the scale produces the same reading each time), those results are incorrect. this is where validity comes into play. validity refers to the extent to which a given instrument or tool accurately measures what it’s supposed to measure. while any valid measure is by necessity reliable, the reverse is not necessarily true. researchers strive to use instruments that are both highly reliable and valid.