Tracksaws, Inc Formulation:
Let X = Number of Tractors Produced Per Period

question 39

Essay

Tracksaws, Inc. makes tractors and lawn mowers. The firm makes a profit of $30 on each tractor and $30 on each lawn mower, and they sell all they can produce. The time requirements in the machine shop, fabrication, and tractor assembly are given in the table.
$$\begin{array} { l l l l } & \text { Machine Shop } & \text { Fabrication } & \text { Assembly } \\\hline \text { Tractor } & 2 \text { hours } & 2 \text { hours } & 1 \text { hour } \\\text { Lawn Mower } & 1 \text { hour } & 3 \text { hours } & 0 \text { hour } \\\text { Hrs. Available } & 60 \text { hours } & 120 \text { hours } & 45 \text { hours } \\\hline\end{array}$$ Formulation:
Let x = number of tractors produced per period
y = number of lawn mowers produced per period


$\begin{array} { l } \text { MAX 30x+30y } \\\qquad\text { subject to } 2 x + y \quad \leq 60 \\\qquad 2 x + 3 y \quad \leq 120 \\\qquad x \leq 45\end{array}$

The graphical solution is shown below.

-A breakdown in fabrication causes the available hours to drop from 120 to 90 hours. How will this impact the optimal number of tractors and mowers produced?

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Definitions:

Perpetual Inventory System

This is an inventory accounting system where updates are made continuously to the inventory accounts and cost of goods sold as transactions occur, providing real-time inventory information.

Stockouts

A situation in inventory management when the demand or requirement for an item cannot be fulfilled from the current inventory or stock.

Periodic Systems

An inventory system where inventory counts and cost of goods sold calculations are conducted at specific intervals, such as monthly or yearly.

Inventory Shrinkage

The loss of products between acquisition and sale, often due to theft, damage, or errors in inventory management.