00:01
Hello students, today we will discuss about this question.
00:04
In this question we are given that a newspaper boy purchase a paper at purchase at 10 cent and sells them at 15 cents.
00:20
So, however, he is not allowed to return unsold paper if his daily demand is binomial random variable, then here with an is equal to.
00:32
To 10 and p is equals to 1 divide by 3 approximately how many paper should be he purchased so as to minimize his expected profit so to maximize profit we need to find the number of papers he purchased that is equals to question 1 so here first of all suppose the newspaper purchase the new newsboy purchase so here purchase that is m paper since the demand is binomial with n is equal to 10 obviously the profit will be maximized for some m is greater than less than or equals to 10 let p be the profit and d be the demand so here p will be a profit and d that will be a demand so here we can write e of p of p that is equals to summation k is equals to 0 to 10 15 minimum of k m p of d is equals to k minus 10 m so here that is equals to we can write 15 summation k is equals to 0 to m minus 1 k p p of d is equals to k plus 15 m summation k is equal to m to 10, p, d is equal to k minus 10 m.
02:14
Let f of m be a right hand side of the above equation.
02:19
So therefore here f of m is equals to, then we can write here f of m plus 1 that minus f of m that can be given us, that is equals to we will get 15 summation k is equals to m plus 1 to 10, p d is equal to k minus 10 so that is equals to 15 summation k is equal to 0 to m p d is equal to k minus 10 so now we will find the maximum value of m such that fd of m is equal to summation k is equals to 0 to m p of d is equals to k so that is summation of k is equal to 0 to m 10 n ck multiplied by 1 divided by 3 raise to k multiplied by 2 divided by 3 raise to 10 minus k is less than or equals to 1 divided by 3.
03:19
Now we will consider m that is equal to 2.
03:22
So that is equal to fd of 2 that is equal to we will get 10 c 0 1 divided by 3 whole raise to 0 2 divide by 3 whole rise to 10 minus 0 plus up to plus 10 c2, 1 divided by 3 raise to 2, 2 divide by 3 raised to 10 minus 2...