Can someone help me with this please HW 7: The Flowervendor Problem Somebody in
ID: 443659 • Letter: C
Question
Can someone help me with this please
HW 7: The Flowervendor Problem
Somebody in South America sells flower bouquets. Demand for bouquets is randomly distributed:
Demand
Probability
0
3%
1
10%
2
12%
3
35%
4
30%
5
10%
6 or above
0%
Each bouquet costs the flower girl $1,000 pesos to procure, and the retail price is $12,000 pesos. She can salvage unsold flowers $200 per bouquet. Please note than whenever a customer comes and she has stocked out, her loss in prestige (goodwill cost) is equivalent to $1,700 pesos per unsatisfied customer.
Fill the profits in each of the cases in the following table
Demand
Profit
if Q= 0
Profit
if Q= 1
Profit
if Q= 2
Profit
if Q= 3
Profit
if Q= 4
Profit
if Q= 5
0
1
2
3
4
5
Use the values calculated in the above table to obtain expected profits at every level of Q in the table below.
Inventory
Expected Profit
Q = 0
1
2
3
4
5
How many units of inventory (i.e., bouquets) should the flower girl stock to maximize expected profit?
Demand
Probability
0
3%
1
10%
2
12%
3
35%
4
30%
5
10%
6 or above
0%
Explanation / Answer
If Supply = Demand; Profit per Banquet=12000-1000=$11000 peso
If Supply <Demand; Profit per Banquet on extra demand=-$ 1700 peso(loss)
If Supply >Demand; Profit per Banquet on extra supply=200-1000=-$800 peso(loss)
For Demand=2 and supply=3; Supply exceeds demand by 1 unit
Net Profit=2*11000+1*(-800)= 21200
For Demand=3 and supply=2; Demand exceeds Supply by 1 unit
Net Profit=2*11000+1*(-1700)= 20300
With Similar calculation :
Demand
Profit
Profit
Profit
Profit
Profit
Profit
if Q= 0
if Q= 1
if Q= 2
if Q= 3
if Q= 4
if Q= 5
0
0
-800
-1600
-2400
-3200
-4000
1
-1700
11000
10200
9400
8600
7800
2
-3400
9300
22000
21200
20400
19600
3
-5100
7600
20300
33000
32200
31400
4
-6800
5900
18600
31300
44000
43200
5
-8500
4200
16900
29600
42300
55000
Expected demand=0*0.03+1*0.1+2*0.12+3*0.35+4*0.3+5*0.1+6*0=3 unit
For Inventory=1; Profit=1*11000+(3-1)*(-1700)= 7600
For Inventory=4; Profit=3*11000+(4-3)*(-800)= 32200
Inventory(Q)
Expected Profit
0
-5100
1
7600
2
20300
3
33000
4
32200
5
31400
Maximum profit is achieved when inventory=3 unit, where profit=$33000 peso
Demand
Profit
Profit
Profit
Profit
Profit
Profit
if Q= 0
if Q= 1
if Q= 2
if Q= 3
if Q= 4
if Q= 5
0
0
-800
-1600
-2400
-3200
-4000
1
-1700
11000
10200
9400
8600
7800
2
-3400
9300
22000
21200
20400
19600
3
-5100
7600
20300
33000
32200
31400
4
-6800
5900
18600
31300
44000
43200
5
-8500
4200
16900
29600
42300
55000
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