Question

You own a wheat warehouse with a capacity of 20 thousand bushels. At the beginning of month 1, you have 6 thousand

bushels of wheat. Each month, wheat can be bought and sold at the prices per one thousand bushels shown in the table

below.

The sequence of events during each month is as follows:

You observe your initial stock of wheat.

You can sell any amount of wheat up to your initial stock at the current month’s selling price.

You can buy as much wheat as you want, subject to the warehouse size limitation.

Determine how to maximize the profit earned over the next 10 months by finding the quantities to sell and buy each

month. What is your profit?

	selling price	purchase price
month 1	$3	$8
month 2	$6	$8
month 3	$7	$2
month 4	$1	$3
month 5	$4	$4
month 6	$5	$3
month 7	$5	$3
month 8	$1	$2
month 9	$3	$5
month 10	$2	$5

Answer 1

Decision Variables:

Initial stock of wheat

Amount of wheat sold

Amount of wheat bought

The objective is to maximize the profit earned over next 10 months.

Thus, the objective function is,

Maximize

The subjects to constraints are,

Here, the constraints are to maintain capacity and stock levels which are the possible variables with values that the variables of a linear programming problem may take. Constraints are limitation like represent resource constraints. Stock constraints, demand constraint those must be maintained at the maximum or minimum level of condition.

The selling any amount of wheat up to initial stock at the current month selling price and buy as much wheat subject to the warehouse size limitation.