solution

On I-5, you see the bright pink Almond Roca sign. You know about Almond Roca, but you wonder if they have ever thought about Brazil Roca, or Cashew Roca. It turn out they have, and this Tacoma company has a long history and offers a variety of products.

One of the biggest issues facing this company is the rise in prices of raw materials, especially the iconic almond, which due to drought in California has seen a price rise in recent years. In order to diversify their product line, Brown & Haley has started to expand its repertoire to including other nuts, such as cashews and macadamia nuts. They also have a project underway to test a new product line of packaged mixed nuts. Note that this scenario is fictional and the details do not represent actual operations of Brown & Haley.

The company is considering three nut mixes for inclusion in the new product line: Regular Mix, Deluxe Mix, and Holiday Mix. Each mix is made from 5 nuts in different combinations:

• The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts
• The Deluxe Mix consists of 20% of each type of nut
• The Holiday Mix consists of 25% almonds, 15% Brazil nuts, 15% filberts, 25% pecans, and 20% walnuts

An accountant at Brown & Haley completed a cost analysis and determined that the profit contribution per pound is $1.65 for the Regular Mix, $1.90 for the Deluxe Mix, and $2.35 for the Holiday Mix.

Different nuts come from different suppliers. They are shipped in bulk containers and ordering a partial container is not possible. The currently available container sizes and costs are as follows:

One container of each of the types of nuts has been ordered and is on the way.

The sales and marketing teams have projected that initial demand for the different types of mixes will be as follows:

The president of Brown & Haley wants to commit to producing enough of the various mixes to meet the projected initial demand, even if not immediately profitable, in order to introduce these new mixes to the market.

The marketing department is proposing an upgrade to the packaging of the Holiday Mix that would decrease the profit contribution from $2.35 to $2.29 per pound. Would the number of pounds of each type of mix be changed in the optimal solution? (Note that the President would be impressed if you did not need to rerun Solver to answer this question)

If the President’s requirement to meet the initial demand for each type of mix were eliminated would profitability be impacted? If so, by how much?