Linear Programming-Based Workshop Full Employment Calculator

This is an free online production calculator that allows you to set up inequalities (constraints) related to production workshops and find the production quantities that ensure full employment. It also allows for graphical representation.

Workshop Full Employment Calculator

Visualizing Workshop Constraints

Uncolored Workshop Constraint Graph

What is Full Capacity Utilization in Workshops?

Full capacity utilization occurs when all machine (or labor) hours are fully utilized.

For example, a company produces product X in workshop A. Each unit of X requires 2 hours. Workshop A has 100 hours available per month.

If 40 units of X are produced, 40*2 = 80 hours are used. This is underutilization. If 50 units are produced, then 50*2 = 100 hours are used, achieving full capacity utilization.

Why Seek Full Capacity Utilization?

Typically, full capacity utilization is sought to reduce unit costs and increase profits.

Increased Profits with Full Capacity Utilization

For example, a company produces product X in workshop A. Each unit of X requires 2 hours. Workshop A has 100 hours available per month. The profit per unit sold is $5.

Producing 40 units yields a profit of 5*40 = $200. Producing 50 units yields a profit of 50*5 = $250.

Note: This assumes a constant profit per unit, which is not always realistic.

Reduced Unit Costs with Full Capacity Utilization

For example, a company produces product X in workshop A. Each unit of X requires 2 hours. Workshop A has 100 hours available per month. The variable cost per unit is $15, and the fixed monthly cost is $1000.

Producing 40 units results in a unit cost of 15 + 1000/40 = $40. Producing 50 units reduces the unit cost to 15 + 1000/50 = $35.

Notice that as production increases, fixed costs are spread over more units, reducing the unit cost.

If the selling price is $46, producing 40 units yields a profit of $6 per unit or $240 total. Producing 50 units yields a profit of $11 per unit or $550 total. However, producing only 20 units results in a loss per unit of $19 and a total loss of $380.

Full Capacity Utilization and Market Demand

Often, a company may not produce at full capacity due to insufficient market demand.