Exhibit 3-1
a Winemaker in California's Napa Valley Must Decide

question 10

Essay

Exhibit 3-1
A winemaker in California's Napa Valley must decide how much of two types of wine she will produce from a particular variety of grapes. Each liter of table wine yields $8 profit, while each liter of dessert wine produces $3 profit. The labor hours and bottling process time used for type of wine are given in the table below. Resources available include 200 labor hours and 80 hours of bottling process time. Assume the winemaker has more than enough grapes available to supply any feasible production plan.
$$\begin{array} { | l l l | } \hline & \text { Table } & \text { Dessert } \\\hline \text { Labor (Hours) } & 0.20 & 0.60 \\\text { Process Time (Hours) } & 0.30 & 0.10 \\\hline\end{array}$$ ​
-[Part 2] Refer to Exhibit 3-1.Using the graphical solution method,find an optimal solution to the model in Part 1 and determine the maximum profit.

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Definitions:

Value

The importance, worth, or usefulness of something or a numerical quantity assigned to a variable.

Type II Error

The error made in statistical testing when a false null hypothesis is not rejected.

Null Hypothesis

A default hypothesis that there is no significant difference or relationship between specified populations or phenomena, used as a starting point for statistical testing.

Incorrect Decision

A decision based on data analysis or hypothesis testing that incorrectly accepts the null hypothesis or wrongly rejects it, leading to a Type I or Type II error.