Linear Programming Applications
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A certain property can have a maximum of 400 animals. Sheep bought at $120 and sold for $260. Goats are bought at $200 and sold for $400. There is a minimum order of 20 sheep and 30 goats.
By drawing a linear programming graph determine the maximum profit.
| \begin{align} &\text{Points are:}\\ &(30,20),(30,370) \text{ and } (380,20)\\ &\begin{aligned} \text{ Let } x&=\text{Number of goats}\\ y&=\text{Number of sheep} \end{aligned}\\ &\text{The Objective function is}\\ &\qquad P=200x+140y\\ &\text{At }(30,20) \quad\;\; P=8800\\ &\text{At }(30, 370) \quad P=57800\\ &\text{At }(380,20) \quad P=78800\\ &\therefore \text{ Maximum profit}=78800 \end{align} |
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