The optimal number of each type of baseball bat to be produced is
given by linear programming.
(a) The variables are;
- <em>x</em> is for the number of Homer-Hitter manufactured
- <em>y</em> is for the number of Big Timber manufactured
(b) The objective quantity is profit
- The equation for the objective quantity is; P = 17·x + 29·y
(c) The system of inequalities are;
- 8·x + 5·y ≤ 80, which gives; y ≤ 16 - 1.6·x
- 2·x + 5·y ≤ 50, which gives; y ≤ 10 - 0.4·x
(d) Please find attached the graph of the system of inequalities created with MS Excel;
- The vertex points are;
(e) The number of each type to be produced to maximize profit are;
- <u>5 Homer-Hitter and 8 Big Timber</u>
- <u>The maximum profit is $317</u>
<h3>Methods used for the linear programming</h3>
Time to trim and turn the Homer-Hitter = 8 hours
Time it takes to finish the Homer-Hitter = 2 hours
Profit each Homer-Hitter sold, makes = $17
Time to trim and turn the Big Timber = 5 hours
Time to finish the Big Timber = 5 hours
Profit each Big Timber sold, makes = $29
Total available time for trimming and lathing = 80 hours
Total time for finishing = 50 hours
(a) The variables to be used to describe the constraints in the situation are;
- <u>Variable </u><u><em>x</em></u><u> represents the Homer-Hitter</u>
- <u><em>y</em></u><u> represents the Big Timber</u>
(b) A general objective of a manufacturing company is profit, and the objective equation is therefore;
- <u />
(c) The system of inequalities which describes the given constraints are presented as follows;
(d) The equations for the graph are therefore;
Which gives;
The vertices of the feasible region are;
- Please find attached the graph of the above system of inequalities created with MS Excel
(e) The profits at the margins of the feasible region are;
Profit at (0, 10), P = 17 × 0 + 29 × 10 = 290
Profit at (5, 8), P = 17 × 5 + 29 × 8 = 317
Profit at (10, 0), P = 17 × 10 + 29 × 0 = 170
Profit at (0, 0), P = 17 × 0 + 29 × 0 = 0
Therefore, the for maximum profit, the number of each type to be produced are;
- <u>5 Homer-Hitter and 8 Big Timber baseball bats</u>
- The maximum profit is; <u>$317</u>
<em>The above responses are based on the order and questions obtained from a similar online uploaded question.</em>
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Learn more about linear programming here:
brainly.com/question/15356519