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Chapter 5: Problem 8

Sketch the graph of the inequality. $$x<4$$

Short Answer

Expert verified
The graph of the inequality \(x<4\) is a vertical line at x=4 with the area to the left shaded to represent all x-values less than 4.

Step by step solution

01

Identify the Line

First we need to draw the line x = 4. On the x-axis, find the point that represents 4. This line is a vertical line that goes through this point.
02

Determine the Inequality Region

Since the inequality sign is '<', the area that satisfies the inequality is the area lying to the left of the line x=4. If the inequality sign was '>', we would shade to the right of the line.
03

Shade the Appropriate Region

Color the area to the left of the line. This colored area represents all the x-values that are less than 4 in accordance with our inequality.

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Most popular questions from this chapter

Optimal Profit A manufacturer produces two models of elliptical cross-training exercise machines. The times for assembling, finishing, and packaging model \(\mathrm{A}\) are 3 hours, 3 hours, and \(0.8\) hour, respectively. The times for model B are 4 hours, \(2.5\) hours, and \(0.4\) hour. The total times available for assembling, finishing, and packaging are 6000 hours, 4200 hours, and 950 hours, respectively. The profits per unit are \(\$ 300\) for model \(A\) and $$\$ 375$$ for model \(B\). What is the optimal production level for each model? What is the optimal profit?

Computers The sales \(y\) (in billions of dollars) for Dell Inc. from 1996 to 2005 can be approximated by the linear model \(y=5.07 t-22.4, \quad 6 \leq t \leq 15\) where \(t\) represents the year, with \(t=6\) corresponding to 1996\. (Source: Dell Inc.) (a) The total sales during this ten-year period can be approximated by finding the area of the trapezoid represented by the following system. \(\left\\{\begin{array}{l}y \leq 5.07 t-22.4 \\ y \geq 0 \\ t \geq 5.5 \\ t \leq 15.5\end{array}\right.\) Graph this region using a graphing utility. (b) Use the formula for the area of a trapezoid to approximate the total sales.

Graph the solution set of the system of inequalities. $$\left\\{\begin{array}{l}x>y^{2} \\ x

Objective function: $$ z=4 x+5 y $$ Constraints: $$ \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ x+y & \geq 8 \\ 3 x+5 y & \geq 30 \end{aligned} $$

Sketch the region determined by the constraints. Then find the minimum anc maximum values of the objective function and where they occur, subject to the indicated constraints. Objective function: $$ z=7 x+8 y $$ Constraints: $$ \begin{aligned} x & \geq 0 \\ y & \geq 0 \\ x+2 y & \leq 8 \end{aligned} $$
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