Lost Maples Winery Makes Three Varieties of Contemporary Mission Hill

Essay

Lost Maples Winery makes three varieties of contemporary Mission 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.
$$\begin{array} { | l | c | c | c | c | c | } \hline & \begin{array} { c } \text { Grapes } \\\text { Variety A } \\\text { bushels }\end{array} & \begin{array} { c } \text { Grapes } \\\text { Variety B } \\\text { bushels }\end{array} & \begin{array} { c } \text { Sugar } \\\text { KGS }\end{array} & \begin{array} { c } \text { Labour (man- } \\\text { hours) }\end{array} & \begin{array} { c } \text { Contrib. } \\\text { per case }\end{array} \\\hline\text { Austin Formation } & 5 & 0 & 2 & 3 & \$ 24 \\\hline \text { Ste. Genevieve } & 0 & 4 & 0 & 1 & \$ 28 \\\hline \text { Los Alamos } & 2 & 2 & 2 & 4 & \$ 20 \\\hline\end{array}$$ The winery has 2900 bushels of Variety A grapes, 2080 bushels of Variety B grapes, 900 pounds of sugar, and 1260 man-hours of labour available during the next week. The firm operates to achieve maximum contribution.
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?