Math Problem Statement

For the next quarter, the sales volumes will be as follows: January 1,200; February 1,500; March 1,300. The opening finished goods inventory in volumes is 300. The expected closing finished goods inventory (at the end of March) is 500. Each product requires 4 machine hours. The number of monthly available machine hours is 5,200. The company will use the regular production process. Do you think there is insufficient capacity? If yes, indicate the number of machine hours you think will be missed each month. If no, enter zero (0).

Solution

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Given dataLet's break down the information from the image and solve the problem:

Given

  • Sales volumes per month:
    • January: 1,200 units
    • February: 1,500 units
    • March: 1,300 units
  • Opening finished goods inventory: 300 units
  • Expected closing finished goods inventory: 500 units
  • Each product requires 4 machine hours.
  • Monthly available machine hours: 5,200 hours
  • The company will use a regular production process.

Approach:

We need to determine if the machine hours are sufficient for production. We will:

  1. Calculate the production requirements for each month, accounting for inventory.
  2. Determine the total machine hours needed for each month.
  3. Compare this with the available machine hours (5,200 per month) to see if there's a shortfall.

Step 1: Determine the required production volumes

The production volume for each month can be calculated using the formula: Production=(Sales volume+Closing inventory)Opening inventory\text{Production} = (\text{Sales volume} + \text{Closing inventory}) - \text{Opening inventory} However, since the opening and closing inventory apply to the whole quarter, we will adjust for each month.

Step 2: Calculate machine hours for production

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Math Problem Analysis

Mathematical Concepts

Production capacity calculation
Inventory management
Time management

Formulas

Required production = (Sales volume + Closing inventory) - Opening inventory
Total machine hours = Required production * Machine hours per product

Theorems

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Suitable Grade Level

University-level (business management or operations management)