Page $1$:

$1$

Page $2$:

$2$

Page $3$:

$3$

Page $4$:

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Match the scatterplot to the most appropriate correlation coefficient.

$$

$0\mathrm{.}942$

$-0\mathrm{.}901$

$0\mathrm{.}612$

$-0\mathrm{.}724$

The Pinewood Fumiture Company produces chairs and tables from two resources$-$labor and wood. The company has $80$ hours of labor and $36$ board$-$ft$.$ of wood available each day. Demand for chairs is limited to $6$ per day. Each chair requires $8$ hours of labor and $2$ board$-$ft$.$ of wood, whereas a table requires $10$ hours of labor and $6$ board$-$ft$.$ of wood. The profit derived from each chair is $$400$ and from each table, $$100.$ The company wants to determine the number of chairs and tables to produce each day in order to maximize profit.

a$.$ Formulate a linear programming model for this problem.

b$.$ Solve this model by using graphical analysis.

For Problem $5$:

a$.$ How much labor and wood will be unused if the optimal numbers of chairs and tables are produced?

b$.$ Explain the effect on the optimal solution of changing the profit on a table from $$100ws500$