A production function is a mathematical representation of the relationship between inputs and outputs in the production process. It shows how much output can be produced from a given set of inputs.

Short run production function refers to the production process where at least one input is fixed, while others can be varied. For example, in a bakery, the oven and the baking trays are fixed inputs, while the amount of flour, sugar, and other ingredients can be varied. In the short run, the firm can increase output by increasing the variable inputs, but the fixed inputs cannot be changed.

Long run production function refers to the production process where all inputs can be varied. In the long run, the firm can change the size of the plant, the number of workers, and the amount of capital equipment. The long run production function shows the maximum output that can be produced with any combination of inputs.