A grocer\'s daily profit from the sale of two brands of cat food is a) Use margi
ID: 1888784 • Letter: A
Question
A grocer's daily profit from the sale of two brands of cat food is
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 one cent, but keeps the price of the second brand unchanged.
Answer:cents
b) What is the actual change in profit when the price is changed as in part (a)?
Answer:cents
A grocer's daily profit from the sale of two brands of cat food is cents, where x is the price per can of the first brand and x is the price per can of the second, each in cents. Currently the first brand sells for 63 cents per can and the second for 34 cents per can. 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 one cent, but keeps the price of the second brand unchanged. Answer:cents b) What is the actual change in profit when the price is changed as in part (a)? Answer:Explanation / Answer
A) P(x, y) = (x-50)(50-6x+8y)+(y-20)(88+3x-8y) = -6x^2-8y^2 + 11xy +290x -152y - 4260 partial differentiate w.r.t. x Px = -12x +11y+290 for x = 63 cents per can we get profit Px1 = -92 cents for 1cent increase Px2 = -104 cents the change in profit P = Px2-Px1 = -104+92 =-12 cents B) to find actual change substitute x= 63 , y=34 in given eq. We get P(x,y)1 = -658 cents if x = 64 ,y = 34 P(x,y)2 = -756 cents actual change = P(x,y)2-P(x,y)1 =-98 cents
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