The Mason Wine Company produces two kinds of wine – Mason Blanc
and Mason Merlot. The wines are produced in 1,000-gallon batches.
The profit for a batch of Blanc is $12,000 and the profit for a
batch of Merlot is $9,000. The wines are produced from 64 tons of
grapes that the company has acquired. A 1,000-gallon batch of Blanc
requires 4 tons of grapes and a batch of Merlot requires 8 tons.
However, the production is limited by the availability of only 50
cubic yards (yd3) of storage space for aging and 120 hours of
processing time. Each batch of each type of wine requires 5 yd3 of
storage space. The processing time for a batch of Blanc is 15 hours
and the processing time for a batch of Merlot is 8 hours. The wine
company will not produce more or less than the range of amounts
demanded for each type. Demand for each type of wine is for at
least 1 batch but is limited to not more than 7 batches. Even so,
the demand for Blanc is the same as or is higher than the demand
for Merlot. Company executives do not want to depend on just one
type of wine so they have mandated minimum production levels of
both types of wine. Specifically, at least 20% of the total wine
production must be Merlot. Likewise, at least 20% of the total wine
production must be Blanc. Moreover, the amount of the Merlot
produced should not be more than half of the total production.
Also, the break-even point on profit is $54,000. Therefore, company
requires that it must make at least $54,000 in profit to do better
than just break even (that is, profit must be $54,000 or more). The
company wants to set the production levels, in terms of the number
of 1,000-gallon batches of both the Blanc and Merlot wines to
produce so as to earn the most profit possible. (NOTE: Partial
[i.e., fractional] batches can be produced; they refer to pending
production. If fractional, round the optimal solution values to two
(2) decimal places.)
3. Determine the
optimal solution with the graphical solution method consisting of
the following steps:
Graph all of the constraints.
Identify and label the feasible region.
On top of the graph of the feasible region, overlay contours of
the objective function to determine and identify the optimizing
direction.
Identify and label the corner containing the optimal
solution.
Explain why the optimal solution is located at this
corner.
In a space created below this
part, present a copy of your labeled graph.
4. Based on part 3,
calculate and explicitly state in lines entered
below this part the optimal solution and
the optimal value.
5. Explicitly state in
plain language in lines entered below this
part the optimal numbers of batches of Merlot and Blanc
wines to make and the maximum amount of the profit.