A chain of supermarkets has just received the last shipment of strawberries of the season,

packed in cases containing 24 punnets each. From past observations, the fresh fruit

marketing manager is able to develop the following table of total sales revenues (in euros)

for allocating n cases to each of the 6 stores of the chain:

Store 1 2 3 4 5 6

Allocation: 1 case 36 36 32 30 30 29

2 cases 70 68 64 60 58 57

3 cases 95 96 96 90 84 84

4 cases 112 116 128 118 105 104

5 cases 122 125 152 138 126 118

6 cases 122 125 172 153 135 125

7 cases 122 125 181 160 135 125

8 cases 122 125 181 160 135 125

The difference in revenues is due to differences of location and customer propensity to buy

strawberries. Each case has a cost of i20. Use a greedy algorithm for the following

situation:

(a) If there is no restriction on the number of cases that can be obtained, how many cases

should be purchased to at least break even? How many are allocated to each store?

What is the total gross profit (difference between revenue and cost)?

(b) If the maximum number of cases that the manager can procure is 16, how should they

be allocated to the various stores? What is the total revenue? What is the shadow price

of case 17?