Sweet Grape Company (SGC) – Statistics Assignment Help

Assignment Task

 

Sweet Grape Company (SGC) sells bags of grapes and cartons of grape juice. SGC grades grapes on a linear scale of 1 (poor) to 10 (excellent). At present, SGC has on hand 100,000 pounds of Grade 9 grapes and 120,000 pounds of Grade 6 grapes. The average grade of grapes sold in bags must be at least 7, and the average grade of the grapes used to produce grape juice must be at least 8. Each pound of juice yields revenue of $1.50 and incurs a variable processing cost of $1.05. Each pound of grape sold in bags yields revenue of $0.50 and incurs a variable processing cost of $0.20.
Develop a conceptual formulation of an optimization model that Sweet Grape Company (SGC) can use to maximize their profit. Then, implement the model in Excel and answer the following questions.
Consider each question below separately, i.e., independent of each other. (Multiple choice)

What is the optimal profit?
Not possible to calculate with the given information
$67,000
78,000
88,000
What is the total amount of juice production in the optimal solution?
60,000 lbs70,000 lbs75,000 lbs80,000 lbsIn the optimal solution, the value of one additional unit of Grade 9 grapes is 4 times larger than the value of one additional unit of Grade 6 grapes
True
False
What would be the change in the optimal value of the objective function if SGC had 10,000 lbs more Grade 9 Grapes?
There will be no change in the objective function
We cannot calculate this
$6,000
$4,500