The Molokai Nut Company MNC makes four different products fr

The Molokai Nut Company (MNC) makes four different products from macademia nuts grown in the Hawaiian Islands: chocolate-coated whole nuts (Whole), chocolate-coated nut clusters (Cluster), chocolate-coated nut crunch bars (Crunch), and plain roasted nuts (Roasted). The company is barely able to keep up with the increasing demand for these products; however, increasing raw material prices are forcing MNC to watch its margin to ensure it is operating in the most efficient manner possible.
To meet marketing demand for the upcoming week, MNC needs to produce at least 1,000 pounds of the Whole product, between 400 and 500 pounds of the Cluster product, no more than 150 pounds of the Crunch product, and no more than 200 pounds of the Roasted product. Each pound of the Whole, Cluster, Crunch, and Roasted product contains, respectively, 60%, 40%, 20%, and 100% macademia nuts, with the remaining weight made of chocolate coating.
The company has 1,100 pounds of nuts and 800 pounds of chocolate available for use in the next week. The various products are made using four different machines that hull the nuts, roast the nuts, coat the nuts with chocolate (if needed), and package the products. Each machine can be operated for 60 hours during the week. The required processing times, revenues, and variable costs for the products are shown in the tables below.

Minutes Required per Pound

Machine Whole Cluster Crunch Roasted

Hulling 1.00 1.00 1.00 1.00

Roasting 2.00 1.50 1.00 1.75

Coating 1.00 0.70 0.20 0.00

Packaging 2.50 1.60 125 1.00

Per Pound Revenue and Costs

Whole Cluster Crunch Roasted

Selling Price $7.50 $6.00 $4.80 $6.75

Variable Cost $4.73 $3.90 $3.24 $4.65

a. Provide a complete algebraic formulation to determine the product mix that maximizes next week’s profit for MNC. Define the variables and write down the objective function and all constraints mathematically.
b. Create a spreadsheet model for this problem and solve with Excel Solver.
c. What is the optimal solution? What is the optimal value?

Solution

Product mix, also known as product assortment, refers to the total number of product lines that a company offers to its customers. For example, a small company may sell multiple lines of products. Sometimes, these product lines are fairly similar, such as dish washing liquid and bar soap, which are used for cleaning and use similar technologies. Other times, the product lines are vastly different, such as diapers and razors. The four dimensions to a company\'s product mix include width, length, depth and consistency.

Width

The width of a company\'s product mix pertains to the number of product lines that a company sells. For example, if a company has two product lines, its product mix width is two. Small and upstart businesses will usually not have a wide product mix. It is more practical to start with some basic products and build market share. Later on, a company\'s technology may allow the company to diversify into other industries and build the width of the product mix.

Length

Product mix length pertains to the number of total products or items in a company\'s product mix, according to Philip Kotler\'s textbook \"Marketing Management: Analysis, Planning, Implementation and Control.\" For example, ABC company may have two product lines, and five brands within each product line. Thus, ABC\'s product mix length would be 10. Companies that have multiple product lines will sometimes keep track of their average length per product line. In the above case, the average length of an ABC Company\'s product line is five.

A) For maximizing the next week\'s profit MNC should produce =Whole Nut( profit=$ 2.77 Per unit) Cluster (profit=$2.10 per unit) Roasted (Profit=2.10 Per unit) less amount of Crunch( profit=$ 12.56 per unit)