Question

Butter

Quart Industries produces a variety of bottled food products at its various plants. At its Americus plant, it produces two products, peanut butter and apple butter. There are two scarce resources at this plant: packaging capacity and sterilization capacity. Both have a capacity of 40 hours per week. Production of 1000 jars of peanut butter requires 4 hours of sterilizer time and 5 hours of packaging time, whereas it takes 6 hours of sterilizer time and 4 hours of packaging time to produce 1000 jars of apple butter. The profit contributions per 1000 jars for the two products are

$1100 and $1300, respectively. Apple butter preparation requires a boil-down process best done in batches of at least 5000 jars. Thus, apple butter production during the week should be either 0, or 5000 or more jars. How much should be produced this week of each product? What is the profit?

Please show and explain using solver

Answer 1

Let the no. of Peanut butter jar (in 1000s) be x and Apple butter (in 1000s) be y

Total Profit = 1100x + 1300y

We have to maximize this profit

Subject to Constraints

4x + 6y <= 40.........Constraint for hours available for sterilization

5x + 4y <= 40.........Constraint for hours available for packaging

Case-1

y >= 5....................Constraint for minimum production of apple butter jars (in 1000s)

Case-2

y = 0

We solve the above cases as shown below:

Case-1:

Profit for Case-1 = $9250

Case-2:

The profit for Case-2 = $8800

Since profit for Case-1 is more, we will select case-1

The above solution for Case-1 in the form of formulas along with Excel Solver extract is shown below for better understanding and reference:

No. of Peanut Butter Jars = 2.5 * 1000 = 2500

No. of Apple Butter Jars = 5 * 1000 = 5000

Total Profit = $9250

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