FROM FRACTIONS TO UNITS: THE INVENTORY MATH THAT PROCUREMENT TEAMS SKIP

The Business Problem

Two purchasing managers are restocking inventory for an upcoming product launch. The operations manager placed orders for 7/8 of a case of wireless earbuds and 3/4 of a case of phone chargers. The marketing manager placed a single order for 1½ cases of branded accessories. Each case holds 16 units. Which manager ordered more inventory in total, and by how many units?

• a) The marketing manager, 10 units
• b) The operations manager, 2 units
• c) The operations manager, 10 units

Can you figure it out by reading the following program?

from fractions import Fraction

def compare_inventory_orders(order1, order2, mixed_order, units_per_case):
    ops_total = order1 + order2
    ops_units = ops_total * units_per_case
    mkt_units = mixed_order * units_per_case
    return int(ops_units), int(mkt_units)

print("=== Inventory Order Comparison ===")
print("Enter the operations manager's two fractional case orders.")
num1 = int(input("  Order 1 — numerator: "))
den1 = int(input("  Order 1 — denominator: "))
num2 = int(input("  Order 2 — numerator: "))
den2 = int(input("  Order 2 — denominator: "))
print("Enter the marketing manager's order as a mixed number.")
whole = int(input("  Whole part: "))
num3 = int(input("  Fraction — numerator: "))
den3 = int(input("  Fraction — denominator: "))
units_per_case = int(input("Units per case: "))

order1 = Fraction(num1, den1)
order2 = Fraction(num2, den2)
mixed_order = whole + Fraction(num3, den3)

ops, mkt = compare_inventory_orders(order1, order2, mixed_order, units_per_case)
diff = abs(ops - mkt)
winner = "Operations manager" if ops > mkt else "Marketing manager"
print(f"\nOperations manager total: {ops} units")
print(f"Marketing manager total:  {mkt} units")
print(f"Winner: {winner} ordered more — difference: {diff} units")