To find: The manufacturer’s maximum profit and combination of shoes for the maximum profit.
Answer to Problem 27SGR
Therefore, to obtain maximum profit the company must produce 12 pairs of outdoor and 16 pairs of indoor shoes. The maximum profit is
Explanation of Solution
Given information :
Total hours needed for Step 1 is
Total hours needed for Step 3 is
Calculation :
Consider to obtain maximum profit the company must make x set of outdoor and y pair of indoor shoes.
For manufacturing a set of outdoor shoes requires 2 hours in step one and 1 hour in step two whereas for indoor shoes requires 1 hour of step one 3 hours of step two.
Therefore:
Total hours needed for Step 1 is
Total hours needed for Step 3 is
Consider the company has labors for 40 hour in Step 2 and 60 hour in Step 2 therefore:
And obviously:
As the company earns
Subject to the conditions:
Draw the feasible region bounded by the above inequalities as below:
Consider
As
As
Compute the objective function
Therefore,
Therefore, to obtain maximum profit the company must produce 12 pairs of outdoor and 16 pairs of indoor shoes. The maximum profit is
Chapter 3 Solutions
Glencoe Algebra 2 Student Edition C2014
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