A grocer\'s daily profit from the sale of two brands of cat food is P(x,y)=(x-60

Question

A grocer's daily profit from the sale of two brands of cat food is P(x,y)=(x-60)(50-6x+6y)+(y-70)(38+3x-6y) cents, where x is the price per can of the first brand and y is the price per can of the second, each in cents. Currently the first brand sells for 85 cents per can and the second for 88 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: cents

Explanation / Answer

a) differentiate P to find dP=(x-60)(-6)+(50-6x+6y)+(y-70)3 replace x=86 and y=88 to find the value of dP.the equation dP comes like this because here dx(change in x=1) and dy=0,rest is basic differentiation rule

b)the intial profit on replacing the values in the equation comes out to be -2530 and on replacing x by 86 and y by 88 we get the answer as -2564(I guess the equation is wrong) subtract initial from final to find the actual change in profit.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.