The demand for an item over the next four quarters is 280, 400, 450, and 300 units, respectively. The price per unit starts at $20 in the first quarter and increases by $1 each quarter thereafter. The supplier can provide no more than 400 units in any one quarter.

Although we can take advantage of lower prices in early quarters, a storage cost of $3.80 is incurred per unit per quarter. In addition, the number of units that can be held over from one quarter to the next must be 80 or less. Develop an LP model to determine the optimum schedule for purchasing the item to meet the demand, and find the optimum solution using AMPL, Solver, or TORA.