Product Regular mix Deluxe mix Holiday mix Ingredient Almond Brazil nut Filbert Pecan Walnut 15% 25% 25% 10% 25% 20% 20% 20% 20% 20% 25% 15% 15% 25% 20% Product Profit $1.65 $1.90 $2.35 Demand (lb) 10,000 5,000 3,000 er Ingredient Availability (lb) Cost 6,000 $7,800 7,500 $7,350 7,500 $7,150 6,000 $7,200 7,500 $7,450 Decision variables Production quantity in lbs Regular mix Deluxe mix Holiday mix Objective function Maximize profits Constraints Availability of ingredients Consumption CH Almond Brazil nut Filbert Pecan Walnut Availability 6,000 7,500 7,500 6,000 7,500 Demand to satisfy Produced Regular mix Deluxe mix Holiday mix XXX Demand 10,000 5,000 3,000 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 $1.65 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: 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