If a bank that desires to hold no excess reserves and has just enough reserves to meet the required reserve ratio of 15 percent
1 answer:
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Answer:
See explanation below.
Explanation:
Let X the random variable that represent the demand for the magazine, the pmf for X is given by:
X 1 2 3 4 5 6
P(X) 1/15 2/15 3/15 4/15 3/15 2/15
3 magazines
For this case the total spent is 2*3 = $ 6
And the net revenue for this case would be:
$4-$6 = -$2 , X=1 (demand 1)
$4*2-$6 = $2 , X=2 (demand 2)
$4*3-$6 = $6 , X=3 (demand 3)
For the values of X=4,5,6 the net revenue will be $6 since the number of magazines is 3
And the expected value for the net revenue would be:
4 magazines
For this case the total spent is 2*4 = $ 8
And the net revenue for this case would be:
$4-$8 = -$4 , X=1 (demand 1)
$4*2-$8 = $0 , X=2 (demand 2)
$4*3-$8 = $4 , X=3 (demand 3)
$4*4-$8 = $8 , X=4 (demand 4)
For the values of X=5,6 the net revenue will be $8 since the number of magazines is 4
And the expected value for the net revenue would be:
As as we can see we have a higher expected value for the case with 4 magazines.
Answer:
a. 54
b. 810 dollars
c. 390 dollars
d. 75 pictures
e. 561.6 dollars and 562.5 dollars
f. 38 pictures
Explanation:
demand per week = 18 pictures
annually this demand = 18 *52 = 936
charge per unit = 60 dollars
order for 6 weeks = 6*18 = 108 quantities
cost of ordering = 45 dollars
cost of holding annually = 15 dollars
a. current average inventory
= (18*6)/2
= 54 pictures
b. current annual holding cost
(108/2)*15
= 810 dollars
c. current annual holding cost
= 936/108 * 45
= 390 dollars
d. size orders to be placed
=
=
= 74.9
≈ 75 pictures have to be ordered
e. ordering holding cost per picture
936/75 * 45
= 561.6 dollars
and inventory holding cost per picture
= 75/2 * 15
=562.5 dollars
f. shop inventory per year at optimal ordering quantity
= 75/2
= 37.5
≈ 38 pictures