A Beverage Can Manufacturer Makes 3 Sizes of Soft Drink

A beverage can manufacturer makes 3 sizes of soft drink cans-Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day.The following table provides the details of the input needed to manufacture one batch of 100 cans for each size
​ $\begin{array}{lcccc} &&cans\\& \text { Large } & \text { Medium } & \text { Small } & \text { Maximum } \\\hline \text { Metal (kg)/batch } & 9 & 6 & 5 & 120 \\\text { Machines' Time (hr)/batch } & 4.4 & 4.2 & 4 & 90 \\\text { Profithatch } & \$ 50 & \$ 45 & \$ 42 &\end{array}$ ​
Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced.

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Let L = number of batches of Large can...

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