The Alfredo Fragrance Company produces only one product, a perfume called Hint of Elegance. Hint of Elegance consists of two secret ingredients blended into an exclusive fragrance, which is marketed in Zurich. An economic expression referred to as the Cobb-Douglas function describes the production of Hint of Elegance as follows: Where X is the amount of perfume produced. The company operates at a level where ingredient 1 is set daily at 25 units and ingredient 2 at 36 units. Although the price Alfredo pays for ingredient 1 is fixed at $50 per unit, the cost of ingredient 2 and the selling price for the final perfume are both probabilistic. The sales price for Hint of Elegance follows this distribution: SALES PRICE ($) PROBABILITY 300 0.2 350 0.5 400 0.3 The cost for ingredient 2 is Ingredient 2 Cost ($) Probability 35 0.1 40 0.6 45 0.3 (a) What is the profit equation for Alfredo Fragrance Company?
The Alfredo Fragrance Company produces only one product, a perfume called Hint of Elegance. Hint of Elegance consists of two secret ingredients blended into an exclusive fragrance, which is marketed in Zurich. An economic expression referred to as the Cobb-Douglas function describes the production of Hint of Elegance as follows:
Where X is the amount of perfume produced.
The company operates at a level where ingredient 1 is set daily at 25 units and ingredient 2 at 36 units. Although the price Alfredo pays for ingredient 1 is fixed at $50 per unit, the cost of ingredient 2 and the selling price for the final perfume are both probabilistic. The sales price for Hint of Elegance follows this distribution:
|
SALES PRICE ($) |
PROBABILITY |
|
300 |
0.2 |
|
350 |
0.5 |
|
400 |
0.3 |
The cost for ingredient 2 is
|
Ingredient 2 Cost ($) |
Probability |
|
35 |
0.1 |
|
40 |
0.6 |
|
45 |
0.3 |
(a) What is the profit equation for Alfredo Fragrance Company?
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