Lost Maples Winery Makes Three Varieties of Contemporary Texas Hill

Essay

Lost Maples Winery makes three varieties of contemporary Texas Hill Country wines: Austin Formation (a fine red), Ste. Genevieve (a table white), and Los Alamos (a hearty pink Zinfandel). The raw materials, labour, and contribution per case of each of these wines is summarized below.
$$\begin{array} { | l | c | c | c | c | c | } \hline & \begin{array} { c } \text { Grapes } \\\text { Variety A } \\\text { bushels }\end{array} & \begin{array} { c } \text { Grapes } \\\text { Variety B } \\\text { bushels }\end{array} & \begin{array} { c } \text { Sugar } \\\text { pounds }\end{array} & \begin{array} { c } \text { Labour (man- } \\\text { hours) }\end{array} & \begin{array} { c } \text { Contrib. } \\\text { per case }\end{array} \\\hline \text { Austin Formation } & 4 & 0 & 1 & 3 & \$ 24 \\\hline \text { Ste. Genevieve } & 0 & 4 & 0 & 1 & \$ 28 \\\hline \text { Los Alamos } & 2 & 2 & 2 & 2 & \$ 20 \\\hline\end{array}$$ The winery has 2800 bushels of Variety A grapes, 2040 bushels of Variety B grapes, 800 pounds of sugar, and 1060 man-hours of labour available during the next week. The firm operates to achieve maximum contribution. Refer to the POM for Windows panels showing the solution to this problem. Answer the following questions.
a. For maximum contribution, how much of each wine should be produced?
b. How much contribution will be made by selling the output?
c. Is there any sugar left over? If so, how much? If not, what is its shadow price (dual value)? Explain what this value means to Lost Maples' management.
d. Interpret the meaning of the lower bound to Labour in the Ranging analysis. That is, explain how the solution would change if the amount of labour fell below that lower value.
e. Interpret the meaning of the upper bound to Los Alamos wine in the Ranging analysis.