How much of each brand of tea should be produced?

The Olde English Tea Company makes two brands of tea, each of which is a blend of tea leaves from several sources. Sophisticated tea drinkers with sensitive noses respond more strongly than other consumers to a tea’s fragrance and taste, so that the firm’s premium brand commands a higher price than its standard brand. The table below lists information on the fragrance and taste ratings of tea leaves from the different sources, as well as the minimum quality standards for the firm’s two brands.

Fragrance Rating                     Taste Rating

Tea leaves from Source A                               90                                            85

Tea leaves from Source B                               85                                            90

Tea leaves from Source C                               80                                            75

Tea leaves from Source D                               75                                            80

Premium brand of Tea                                     85                                            84

Standard brand of Tea                                     77                                            81

Further, the costs and availability of the different sources of tea leaves is as follows:

Pounds Available                    $/pound

Tea leaves from Source A                               1500                               1.05

Tea leaves from Source B                               2500                               0.95

Tea leaves from Source C                               4000                               0.80

Tea leaves from Source D                               5000                               0.70

The total of the direct and indirect costs for preparing, packaging, and shipping each of the two brands of tea to distributors is $0.25 per pound. The wholesale selling price of the teas to the distributors is $2.05/pound for Premium and $1.50/pound for Standard. The tea company can sell as much of each tea as it can produce.

Answer the following questions regarding Olde English Tea. Modifications to the base model are to be considered individually, not cumulatively.

a.   How much of each brand of tea should be produced? How much tea will be used from each source? How much will it cost to purchase tea from each source, and in total? What will be the total profit? Which supplies of tea are exhausted, limiting profit?

b.   How would your answers to part a. change if only 2000 pounds were available from source B?

c.   How would your answers to part a. change if up to 6000 pounds were available from source D?

d.   How would your answers to part a. change if the leaves from source C only cost $.65/pound?

e.   How would your answers to part a. change if the minimum taste rating for Standard tea was only 79?

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