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

question 43

Short Answer

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
Let x = number of tractors produced per period
y = number of lawn mowers produced per period
MAX 30x + 30y
subject to  2x + y ? 60
    2x + 3y ? 120
    x ? 45



The graphical solution is shown below.

-Determine the sensitivity range for the profit for tractors.

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Definitions:

Nash Model

A concept in game theory where each participant's strategy is optimal given the strategies of all other participants, leading to a situation of equilibrium.

Nash Equilibrium

A concept within game theory where no player can benefit by changing strategies while the other players keep theirs unchanged.

Bertrand Model

An economic model of competition among firms that compete by setting prices simultaneously.

Payoff Matrix

A table that shows the payoffs for each player in a game for every possible combination of actions by the players.