Tots Toys Makes a Plastic Tricycle That Is Composed of Three

question 29

Essay

Tots Toys makes a plastic tricycle that is composed of three major components: a handlebar-front wheel-pedal assembly, a seat and frame unit, and rear wheels. The company has orders for 12,000 of these tricycles. Current schedules yield the following information. $$\begin{array} { l | c c c | c | c } \text { Component } & \begin{array} { c } \text { Requirements } \\\text { Plastic }\end{array} & \text { Time } & \text { Space } & \begin{array} { c } \text { Cost to } \\\text { Manufacture }\end{array} & \begin{array} { c } \text { Cost to } \\\text { Purchase }\end{array} \\\hline \text { Front } & 3 & 10 & 2 & 8 & 12 \\\text { Seat/Frame } & 4 & 6 & 2 & 6 & 9 \\\text { Rear wheel (each) } & .5 & 2 & 1 & 1 & 3\\\text { Available }&50000&160000&30000\end{array}$$ The company obviously does not have the resources available to manufacture everything needed for the completion of 12000 tricycles so has gathered purchase information for each component. Develop a linear programming model to tell the company how many of each component should be manufactured and how many should be purchased in order to provide 12000 fully completed tricycles at the minimum cost.

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Definitions:

Variable Costs

Charges that adjust in relation to the quantity of goods or services manufactured by a corporation.

Fixed Costs

Expenses that do not change in response to the level of goods or services produced by the business, such as rent, salaries, and insurance.

Composite Unit

A measurement or quantity combining two or more units to represent a product or system's multiple aspects.

Contribution Margin

The difference between the sales revenue and variable costs of a product, indicating how much contributes to covering fixed costs and earning profit.