Question: A company produces three canned fruit products, referred to as x1, x2, and x3. The main ingredients are pears and peaches. The production process requires mixing, canning, and packaging. The resources required for each product and for each process are shown in the linear programming formulation below.

The objective is to determine the number of units of each to produce to maximize profit. The linear programming solver solution and sensitivity report are shown. Note that part of the information has intentionally been left blank.

Use the information below to answer the following questions. Answer each question independently and separately from all other questions. In each the term ‘solution’ refers to the number of units to produce(x1, x2, and x3) and ‘profit’ refers to the total profit of the solution.

Max Z = 10x1+ 6x2 + 8x3

s.t. 20x1 + 10x2 + 16x3 <= 320 lbs pears

10x1 + 20x2 + 16x3 <= 400 lbs peaches

1x1 + 2x2 + 2x3 <= 43 hours mixing

1x1 + 1x2 + 1x3 <= 60 hours canning

2x1 + 1x2 + 1x3 <= 40 hours packaging

x1, x2, x3 >= 0

Instructions- please read before answering these questions.

In the questions that follow, use only the information available in the sensitivity report provided on the previous page; do not attempt to determine a new solution. The point of this question is to interpret that one sensitivity report. Do not enter the problem into excel or solver. Answer each question independently and separately from all other questions . In each the term ‘ solution ’ refers to the number of units to produce(x1, x2, and x3) and ‘ profit ’ refers to the total profit of the solution.

1. What are the optimal solution and its profit?
2. At optimality, how much slack does each constraint have?
3. Give the range of values for the profit on x2 for which the current solution remains optimal.
4. If the profit on x1 becomes $15, does the solution change? Why?
5. If the profits on x1, x2, and x3 each simultaneously go up by $1, does the solution change? Why? Show work to support your answer .
6. If an additional 10 pounds is added to the available amount of pears, will the solution change? Why?
7. If an additional 10 pounds is added to the available amount of pears, will the total profit change? Why? If yes, what is the new value?
8. If an additional 10 pounds is added to the available amount of pears and an additional 10 pounds is added to the available amount of peaches, will the solution change? Why?
9. If an additional 10 pounds is added to the available amount of pears and an additional 10 pounds is added to the available amount of peaches, will the profit change? If yes, what is the new value? Why? Show work to support your answer .
10. Fill in below the missing information about the packaging constraint.

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Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document