Question

A manufacturer of highly specialized computer components produces two different types, A and B. In any given week, there are 4,000 man-hours of skilled labour available. Each component A requires one man-hour for its production and each component B requires 2 man-hours. The manufacturing plant has the capacity to produce a maximum of 2,250 components of type A each week as well as 1,750 components of type B. Each component A requires 5kg of plate and 2kg

Answer 1

The question involves using mathematics, specifically linear programming, to solve an optimization problem for a manufacturer to determine the number of components A and components B they should produce given constraints like man-hours and production capacities.

Step-by-step explanation:

The student's question involves an optimization problem where the manufacturer needs to determine the number of components A and components B to produce within a given set of constraints, including labor hours and production capacity. This sort of problem is categorized under linear programming, which is part of Mathematics, specifically within operations research or algebra. Utilizing details such as man-hour requirements and production capacities, a model can be formulated to maximize or minimize a particular objective function (e.g., profit, cost, production quantity).

For example, the manufacturer may want to maximize profit while producing components A and B under the constraints of labor hours and production limitations. The constraints would be:

• 1 man-hour for A, 2 man-hours for B, with a total of 4,000 man-hours available.
• Maximum of 2,250 A components and 1,750 B components can be produced weekly.
• Material requirements for each component (e.g., 5kg plate for A).

By setting up these constraints and defining an objective function (like maximizing profit), the manufacturer can use linear programming techniques to determine the optimal production levels of A and B.