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 turns out they have, and this Tacoma company has a long history and offers a variety of products. Current Issues 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 Scenario 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 $$1\mathrm{.}65$ for the Regular Mix, $$1\mathrm{.}90$ for the Deluxe Mix, and $$2\mathrm{.}35$ for the Holiday Mix. Different nuts come from different suppliers. They are shipped in bulk containers and ordering a partial container is not possible. The currently available container sizes and costs are as follows: Type of Nut Container Size $($pounds$)$ Cost per Container Almond $6000$ $$7800$ Brazil $7500$ $$7350$ Filbert $7500$ $$7150$ Pecan $6000$ $$7200$ Walnut $7500$ $$7450$ 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: Type of Mix Orders $($pounds$)$ Regular $10,000$ Deluxe $5,000$ Holiday $3,000$ 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 Analysis Required Answer the following questions: $1.$ Based on current cost information, what is the cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes? $2.$ How much of each type of mix should be made using only the nuts already ordered and keeping in mind the President$$s requirement to meet the initial demand for each type of mix? What is the resulting optimized profit? $3.$ Sometimes small amounts of certain types of nuts become available in secondary markets. Which types of nuts should be pursued in order to increase profit? $4.$ A supplier has offered us $1000$ pounds of almonds for $$1000.$ Should these almonds be purchased? If yes, how much would profits increase? $5.$ A supplier has offered us $1200$ pounds of filberts for $$950.$ Should these filberts be purchased? If yes, how much would profits increase? $6.$ The marketing department is proposing an upgrade to the packaging of the Holiday Mix that would decrease the profit contribution from $$2\mathrm{.}35$ to $$2\mathrm{.}29$ per pound. Would the number of pounds of each type of mix be changed in the optimal solution? $($Note that the President would be impressed if you did not need to rerun Solver to answer this question$)7.$ If the President$$s requirement to meet the initial demand for each type of mix were eliminated would profitability be impacted? If so$,$ by how much? If you use Solver to answer a question, be sure to reference the specific Solver output that supports your answer.