Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200 and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use.

How many rolls of Grade X & Grade Y should be produced to maximize profits?

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.