A deli sells 960 sandwiches per day at a price of $8 each. (A) A market survey s

Question

A deli sells 960 sandwiches per day at a price of $8 each. (A) A market survey shows that for every $0.10 reduction in the price, 20 more sandwiches will be sold. How much should the deli charge in order to maximize revenue? The deli should charge $ for a sandwich to maximize revenue. (B) A different market survey shows that for every $0.20 reduction in the original $8 price, 10 more sandwiches will be sold. Now how much should the deli charge in order to maximize revenue? Now the deli should charge $ for a sandwich to maximize revenue.

Explanation / Answer

A) revenue =price*quatity

let X be the price reduced; hence new quantiy =20X/0.1 =200X

hence revenue R =(960+200X)(8-X) =7680+1600x-960X-200X2

R =7680+640X -200X2

differentiating R and putting it to 0;

400X =640

X =1.6

hence reduced price =8-1.6 =6.4

B) for reduced X price ; quantity increased =10X/0.2 =50X
hence R =(960+50X)(8-X) =7680 +400X-960X-50X2

R =7680 -560X -50X2

differentiating above will give -ve value of X, hence we can not reduce price then 8   

hence dell should charge 8

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