Question

The Business Situation

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.)

7. a. Calculate and explicitly state in lines entered below any amounts of slack/surplus involved in the optimal solution.

b. Interpret in the context of the business situation and in plain language each and every slack/surplus stated above. Add lines below.

8. In lines entered below, identify the active, inactive, and redundant (if any) constraints.

9. In lines entered below, explain how the optimal solution and the optimal value is changed if later it is determined that the break-even point is $64,000 (that is, profit must be $64,000 or more)?

Answer 1

SOLUTION :

A) Decision variable are unknown programming model quantity that was determined by a decision maker by using any optimization method.They are represent the decision that are going to be done by decision maker.

B) Max.12000 x₁ +9000x₂ objective functions

C) With subject to : Constraints

4x₁ +8x₂ 64

5x₁ + 5x₂ 50

15x₁ +8x₂ 120

x₁ 7(max blanc)

x₂ 1(min blanc)

x₂7(max merlot)

x₂1(min merlot)