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Magazine Chapter 3: Q35. (page 144)
35 Wood pulp can be converted to either notebook paper or newsprint. The Canyon Pulp and Paper Mill can produce at most units of paper a day.egular customers require at least 10 units of notebook paper and units of newspaper daily. If the profit on a unit of notebook paper is \(500 and the profit on a unit of newsprint is \), how many units of each type of paper should the mill produce each day to maximize profits?
Short Answer
The maximum profit is $when Mill morenotebook paper no newsprint.
Step by step solution
Step-1 – Define the variables
Number of notebook paper.
Number of newsprint.
Step-2 – Write system of inequalities
Since the number of paper cannot be negative. andmust be nonnegative numbers.
The canyon pulp and paper Mill can produce at most 200 notebooks.
Regular customer requires at leastunits of notebook andunits of newsprint.
and
Step-3 – Graph the system of inequalities
Step-4 –Find the co-ordinate of the vertices of the feasible region
From the graph, the vertices of the feasible region are at, and
Step-5 –Write the function to be maximized or minimized
The function that describe the maximum profit is
Step-6 –Substitute the co-ordinate of the vertices into the function.
Step-7 –Select the greatest result
The maximum value of the function is.This means that the maximum profit is $ when Mill makes-notepaper andnewsprint
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