Ahardware store orders at most $2,500 worth of concrete and sand. the store needs to make a profit of at least $2,750 on the order. the possible combinations of concrete and sand for this order are given by this system of inequalities, where c = pounds of concrete and s = pounds of sand: 6c + 2s ≤ 2,500 4.50c + 3s ≥ 2,750 which graph's shaded region represents the possible combinations of concrete and sand for this order?

The below graph's shaded region represents the possible combinations of concrete and sand for this order

Step-by-step explanation:

Here, the system of inequality that represents the given situation is,

6c + 2s ≤ 2,500 --------(1)

4.50c + 3s ≥ 2,750 -------(2)

Where c = pounds of concrete,

s = pounds of sand

Now, The related equation of the above inequalities are,

6c + 2s = 2500

4.50c + 3s = 2750

By solving the above equations,

We get, ,

Thus, the intersection point of the inequalities =

Now, At (0,0) ,

inequality (1), 6×0 + 2×0≤ 2500 ⇒ 0 ≤ 2500 ( true)

Hence, the shaded region of inequality contains the origin.

Similarly, At (0,0), inequality (2) is false,

⇒ The shaded region of inequality (2) does not contain the origin.

Thus, By the above explanation we can plot the shaded region of the system of the given inequalities.

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.