A factory produces two types of widgets: Widget A and Widget B. Producing one Widget A requires 3 hours of labor, and producing one Widget B requires 2 hours. The factory operates 240 hours a week and wants to produce at least 50 widgets total. If Widget A yields a profit of $30 and Widget B yields a profit of $40, how many of each must be produced to maximize profit?

Thu, 16 Apr 2026 17:34:10 +0000

A factory produces two types of widgets: Widget A and Widget B. Producing one Widget A takes 3 hours of labor, while Widget B takes just 2 hours. With only 240 factory hours available each week, decision-makers face a key challenge—balancing production volume and profitability while meeting a minimum output goal. As manufacturers navigate shifting consumer demand and rising material costs, optimizing widget combinations offers tangible ways to maximize returns within strict labor and volume constraints. This scenario raises a familiar but critical question: how should a factory allocate its limited labor hours to produce two distinct products—each with different production times and profit margins—while meeting minimum weekly output targets? The answer lies not just in math, but in strategic planning that aligns operational efficiency with financial goals. ### Why Is This a Key Industry Challenge? Warehouse and manufacturing trends highlight growing pressure on production lines to do more with less. Labor remains a primary cost, and efficiency is now a top priority across US manufacturing. For factories operating under tight schedules—like the example here with 240 weekly hours—each decision on product mix directly impacts weekly output and profitability. Understanding optimal production ratios helps managers anticipate resource needs, forecast sales, and stay competitive.