To calculate: The number of shoes manufactured to maximize the profit.
Answer to Problem 27SGR
The profit is $480. The company should manufacture 12 outdoor shoes and 16 indoor shoes.
Explanation of Solution
Given information:
Each pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.
40 hours of labor available for step 1 and 60 hours of labor is available for step 2 process.
Calculation:
Consider the provided information thateach pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.
40 hours of labor available for step 1 and 60 hours of labor is available for step 2 process.
Let x denote the number of outdoor shoes and y denote the number of indoor shoes.
Since, each pair of outdoor shoe require 2 hour in step 1 and 1 hour in step 2 and gives a profit of $20. Each pair of indoor shoe require 1 hour in step 1 and 3 hour in step 2 and gives a profit of $15.
And,
Plot the inequalities and shade the common region
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
Substitute
Since, maximum profit is $480. The company should manufacture 12 outdoor shoes and 16 indoor shoes.
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