A green grocer’s daily profit from the sale of two brands of orange juice is given by P(x , y) = (x – 30)(70 – 5x + 4y) + (y – 40)(80 + 6x – 7y) where x is the price per gallon bottle in dollars of the first brand and y is the price per gallon bottle in dollars of the second brand. The profit is also measured in dollars. Currently, the first brand sells for 50 dollars per gallon bottle and the second brand for 52 dollars per gallon bottle. (a) Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises the price of the first brand by fifty cents per gallon bottle but decreases the price of the second brand by seventy-five cents per gallon bottle and find the stationary points of the profit function P(x , y).
A green grocer’s daily profit from the sale of two brands of orange juice is given by
P(x , y) = (x – 30)(70 – 5x + 4y) + (y – 40)(80 + 6x – 7y) where x is the price per gallon bottle in dollars of the first brand and y is the price per
gallon bottle in dollars of the second brand. The profit is also measured in dollars.
Currently, the first brand sells for 50 dollars per gallon bottle and the second brand for 52 dollars per gallon bottle.
(a) Use marginal analysis to estimate the change in the daily profit that will result if
the grocer raises the price of the first brand by fifty cents per gallon bottle but decreases the price of the second brand by seventy-five cents per gallon bottle and find the stationary points of the profit function P(x , y).
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