An appliance store manager is ordering chest and upright freezers. One chest freezer costs $250 and delivers a $40 profit. One upright freezer costs $400 and delivers a $60 profit. Based on previous sales, the manager expects to sell at least 100 freezers. Total prfit must be at least $4800. Find the least number of each type of freezer the manager should order to minimize costs.

To find the least number of each type of freezer the manager should order, we can use a system of linear equations.

Let's assume the number of chest freezers to be ordered is 'x' and the number of upright freezers to be ordered is 'y'.

We have the following information:

Cost of one chest freezer = $250
Profit from one chest freezer = $40

Cost of one upright freezer = $400
Profit from one upright freezer = $60

We need to minimize costs while ensuring that the total profit is at least $4800 and the total number of freezers ordered is at least 100.

The total cost of the ordered freezers can be calculated as:
Cost of chest freezers = $250 * x
Cost of upright freezers = $400 * y
Total cost = Cost of chest freezers + Cost of upright freezers

The total profit from the ordered freezers can be calculated as:
Profit from chest freezers = $40 * x
Profit from upright freezers = $60 * y
Total profit = Profit from chest freezers + Profit from upright freezers

Based on the given conditions, we can form the following equations:

Total cost equation: $250x + $400y = Total cost (1)
Total profit equation: $40x + $60y = Total profit (2)
Number of freezers ordered equation: x + y >= 100 (3)
Total profit constraint: Total profit >= $4800 (4)

Now, we need to convert the problem into a linear programming problem.

Minimize: Total cost

Subject to:
$250x + $400y >= Total cost (1)
$40x + $60y >= Total profit (2)
x + y >= 100 (3)
Total profit >= $4800 (4)

The objective function is to minimize the total cost, and the given conditions and constraints are included as linear equations.

This linear programming problem can be solved using various optimization methods, such as the simplex method or graphical method, to determine the least number of each type of freezer the manager should order to minimize costs.