A Craftsman Builds Two Kinds of Birdhouses, One for Wrens

question 54

Essay

A craftsman builds two kinds of birdhouses, one for wrens (X1), and one for bluebirds (X2). Each wren birdhouse takes four hours of labour and four units of lumber. Each bluebird house requires two hours of labour and twelve units of lumber. The craftsman has available 60 hours of labour and 120 units of lumber. Wren houses profit $6 each and bluebird houses profit $15 each.
Use the software output that follows to interpret the problem solution. Include a statement of the solution quantities (how many of which product), a statement of the maximum profit achieved by your product mix, and a statement of "resources unused" and "shadow prices." $$\begin{array} { | l | r | r | r | r | r | } \hline { \text { Bird Houses Solution } } \\\hline \text { Variable } & \text { Value } & \text { Reduced } & \text { Original Val } & \text { Lower Bound } & \text {Upper Bound } \\\hline X 1 & 12 . & 0 . & 6 . & 5 . & 30 . \\\hline X 2 & 6 . & 0 . & 15 . & 3 . & 18 . \\\hline \text { Constraint } & \text { Dual Value } & \text { sack/Surplus } & \text { Original Val} & \text { Lower Bound } & \text {Upper Bound } \\\hline \text { Constraint 1 } & 0.3 & 0 & 60 . & 20 . & 120 . \\\hline \text { Constraint 2 } & 1.2 & 0 . & 120 . & 60 . & 360 . \\\hline\end{array}$$

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Definitions:

Apoptosis

Programmed cell death; apoptosis is a normal part of an organism’s development and maintenance. Compare with necrosis.

Organelles

Specialized structures within cells that perform distinct processes necessary for cellular function and survival.

Centrioles

Cylindrical structures found in most eukaryotic cells, playing a crucial role in cell division.

Centrosome

The centrosome is an organelle that serves as the main microtubule organizing center in animal cells, playing a crucial role in cell geometry and mitosis.