Note: Write the formula for every question depending upon the requirement.
Calculations: Answer all the questions
Case Problems:
The Saudia Juice Company produces two kinds of Juice—Saudia Nectar and Saudia Red. The juice is produced from 64 tons of grapes the company has acquired this season. A batch (1,000-gallon) of Nectar requires 4 tons of grapes, and a batch of Red requires 8 tons. However, production is limited by the availability of only 50 cubic yards of storage space and 120 hours of processing time. A batch of each type of juice requires 5 cubic yards of storage space. The processing time for a batch of Nectar is 15 hours, and the processing time for a batch of Red is 8 hours. Demand for each type of juice is limited to seven batches. The profit for a batch of Nectar is $9,000, and the profit for a batch of Red is $12,000. The company wants to determine the number of batches of Nectar (x1) and Red (x2) to produce in order to maximize profit.
(Note: Solve using 2 decimal places)
1-Formulate a linear programming model for this problem.
2- Solve this model by using graphical analysis.
3-Identify the feasible region.
4-Find the extreme points and optimal solution .
5-What is the standard form of the linear programming model?
6-How much of slack resource will be left unused at the optimal solution? (2 marks) What are the binding, non-binding and redundant constraints?
7-What would be the effect on the optimal solution, if the profit for a batch of Nectar and Red is $10850 and $10750 respectively?