
To calculate: The profit when the recycling plant maximizes the processing.

Answer to Problem 28PPS
The profit is $23250.
Explanation of Solution
Given information:
Up to 1200 tons of plastic is processed by recycling plant every week. At least 300 tons must be processed for food containers and 450 tons must be processed for drink containers.
For processing food containers the profit is $17.50 per ton and for drink containers it is $20 per ton.
Calculation:
Consider the provided information, up to 1200 tons of plastic is processed by recycling plant every week. At least 300 tons must be processed for food containers and 450 tons must be processed for drink containers.
For processing food containers the profit is $17.50 per ton and for drink containers it is $20 per ton.
Let x denote the number of food containers processed and y denote the number of drink containers processed.
Since, up to 1200 tons of plastic is processed by recycling plant every week. At least 300 tons must be processed for food containers and 450 tons must be processed for drink containers.
Plot the inequalities and shade the common region
The function that is the profit function that is to be maximized is,
Substitute the vertices of the feasible region to find the point at which maximum revenue is there.
Substitute
Substitute
Substitute
Since, maximum profit is $23250 which is when 300 food containers and 900 drink containers are processed.
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