Question

In: Accounting

A certain dealer owns a warehouse that can store a maximum of 600 units of a...

A certain dealer owns a warehouse that can store a maximum of 600 units of a given commodity. He has on hand 100 units of the commodity and knows the buying and selling price for the next 5 time periods. They are:

PERIOD

BUYING PRICE

SELLING PRICE

1

15

16

2

17

17

3

21

20

4

19

19

5

16

20

He is permitted to sell up to the amount that he has in his warehouse at the beginning of each period. If he buys in a given period, delivery will be made so that it is in storage at the beginning of the next period. Let (Xi, Yi) denote the amount he buys and sells in time-period i respectively. What is the optimal buying\selling strategy.

Formulate the linear programming problem.  

Develop a spreadsheet and solve the problem.

Solutions

Expert Solution

See the table below for solution :

As per working given below situation 2 i.e Buying price 17 & Selling price 17 is the best resuting in profit.

Period

Opening

Stock

Purchase price of

Opening Stock

Total Purchase Cost of opening stock

Additional Purchase Qty

Purchase

Price of Additional purchase qty

Total Purchase Cost of additional qty purchased

Total Selling Price

(Restricted to purchase cost of opening stock)

Selling

Price

Sale Qty

Profit (Selling price - Buying Price) * Qty sold

Closing

Stock in Qty

Closing Stock in Value

1

100

15

1500

500

15

7500

1488

16

93

(16-15)*93 = 93

507

7*15 = 105

500*15 = 7500

2

507

15

7605

93

17

1581

7599

17

447

(17-15)*500 = 894

153

60*15 = 900

93*17 = 1581

3

153

15 & 17

2481

447

21

9387

2480

20

124

(20-15)*60 + (20-17)*64 = 492

476

29*17 = 493

447*21 = 9387

4

476

17 & 21

9880

124

19

2356

9044

19

476

(19-17)*29 + (19-21)*457= -856 (loss)

124

124*19 = 2356

5

124

19

2356

476

16

7616

2340

20

117

(20-19)*117 = 117

483

7*19 = 133

476*16 = 7616

ekkarill92 answered 8 months ago
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