A Company Has the Following Usage of Inputs, Constraints on Inputs

question 9

Essay

A company has the following usage of inputs, constraints on inputs and profit margins to make their three products.
$$\begin{array} { l l l l l } \text { Product } & \text { Wiring } & \text { Drilling } & \text { Assembly } & \text { Profit } \\\text { X202 } & 0.47 & 0.28 & 0.55 & 15 \\\text { Y303 } & 0.61 & 0.43 & 0.61 & 18 \\\text { Z404 } & 0.37 & 0.2 & 0.29 & 13.1\end{array}$$ There are maximum amounts of the following: 1625 hours for wiring, 1750 hours for drilling and 1175 hours for Assembly. Make sure that the units produced are integers. Solve for the above problem. The company must make at least 825 X202, 475 Y303 and 625 Z404.
a) How many units of each product will be made?
b) What is the maximum profit?
c) Which input has the least amount of slack?

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Definitions:

Welfare Economics

A branch of economics that focuses on the optimal allocation of resources and goods and aims to evaluate the economic well-being of individuals and society.

Total Surplus

The sum of consumer surplus and producer surplus in a market, representing the total net benefits to all participants in the market transaction.

Demand Curve

A graphical representation showing the relationship between the price of a good or service and the quantity demanded by consumers at those prices.

Supply Curve

A graphical representation showing the relationship between the quantity of a good that producers are willing to sell and the price of the good.