Question: T he Fragrance Coffee Company

The Pilgrim coffee company buys and blends, three types of coffee beans; Brazilian, Peruvian and Colombian. Each kind of bean has its own distinctive aroma and strength, which it uses a taster to rate. The company’s chief taster has developed the following table.

Table 1

Pilgrim Coffee Company wishes to create a blend that has an aroma rating of at least 78 and a strength rating of at least 16. The quantities which are available to the company under a purchase agreement are 1500 pounds of Brazilian beans, 1200 pounds of Colombian beans and 2000 pounds of Peruvian beans.

The aroma rating number is calculated from ratio [1] in which the numbers used comes from Table 1 and: B = pounds used of Brazilian beans, C = pounds used of Colombian beans, P = pounds used of Peruvian beans. To require that the aroma rating be at least some number α, the ratio-condition that follows must be met and is given by [1]

(75B + 60C + 85P) / (B + C + P) >= α (α here is 78) [1]

The strength rating is calculated from ratio [2] using the strength rating numbers from Table 1. To require that the strength rating be at least some number β, the ratio-condition that follows must be met.

(15B + 20C + 18P) / (B + C + P) >= β (β here is 16) [2]

The Pilgrim Company wishes to make 4000 pounds of the blend. It wishes to achieve this at the lowest possible total cost.

1. As the director of all production programs at Pilgrim, you will now determine the quantities of each of the three kinds of coffee beans to purchase such that, while satisfying the aroma and strength rating requirements, and availability requirements, the cost of purchasing is the smallest possible.
2. Calculate the actual achievable aroma and strength rating numbers which your optimal purchasing quantities generate. Do these numbers meet the required aroma and strength ratings?
3. Should competitive conditions require that Pilgrim Coffee Company reduce costs to below the minimum cost of your optimal solution, which of the two rating number requirements (aroma = 78, strength = 16) do you have to alter (increase or decrease to achieve the lower cost)? Describe why the change you propose has the desired result!

Price: $2.99

Solution: The downloadable solution consists of 4 pages
Deliverable: Word Document