A manufacturer produces two types of tables. Each table requires a cabinet maker and a painter to build. The time taken for each worker varies according to the table below.
Let $x$x represent the number of round tables built in a week, and let $y$y represent the number of square tables built in a week.
Cabinet Maker | Painter | |
Round Table | $2$2 hours | $2$2 hours |
Square Table | $2$2 hours | $1$1 hours |
Total time available in a week | $34$34 hours | $30$30 hours |
Finish the set of constraint inequalities below:
Graph the region defined by inequalities 3 and 4 in the first quadrant:
The region of possible solutions that you graphed in part (b) has been sketched more clearly below:
List the four vertices of the feasible region:
$\left(0,0\right),\left(\editable{},\editable{}\right),\left(\editable{},\editable{}\right),\left(\editable{},\editable{}\right)$(0,0),(,),(,),(,)
If a round table sells for a profit of $\$250$$250 and a square table makes a profit of $\$200$$200, write the objective function that models the weekly profit $z$z.
Complete the table below to determine the profit corresponding to each vertex of the feasible region:
Vertex | Profit (dollars) |
$\left(0,0\right)$(0,0) | $0$0 |
$\left(0,17\right)$(0,17) | $\editable{}$ |
$\left(13,4\right)$(13,4) | $\editable{}$ |
$\left(15,0\right)$(15,0) | $\editable{}$ |
Complete the following sentences:
The maximum weekly profit is $\editable{}$ dollars, and occurs at the point $\left(\editable{},\editable{}\right)$(,).
That is to say, $\editable{}$ square tables and $\editable{}$ round tables should be made each week to achieve the maximum profit.
Use curve fitting, log modelling, and linear programming techniques
Apply linear programming methods in solving problems