Aflorist can make a grand arrangement in 18 minutes or a simple arrangement in 10 minutes. the florist makes at least twice as many of the simple arrangements as the grand arrangements. the florist can work only 40 hours per week .the profit on the simple arrangements is $10 and. the profit on the grand arrangements is $25. hind the number and type of arrangements that the florist should produce to maximize profit.

See explanation

Step-by-step explanation:

Let x be the number of simple arrangements and y be the number of grand arrangements.

1. The florist makes at least twice as many of the simple arrangements as the grand arrangements, so

2. A florist can make a grand arrangement in 18 minutes hour, then he can make y arrangements in hours.

A florist can make  a simple arrangement in 10 minutes hour, so he can make x arrangements in hours.

The florist can work only 40 hours per week, then

3. The profit on the simple arrangement is $10, then the profit on x simple arrangements is $10x.

The profit on the grand arrangement is $25, then the profit on y grand arrangements is $25y.

Total profit: $(10x+25y)

Plot first two inequalities and find the point where the profit is maximum. This point is point of intersection of lines and

But this point has not integer coordinates. The nearest point with two integer coordinates is (126,63), then the maximum profit is

step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)