A florist designs two high-profit arrangements— a funeral wreath and a bridal centerpiece. The company’s employees can complete up to 18 arrangements each day using up to 24 total person-hours of labor. It takes 4 person-hours to complete 1 funeral wreath, and 1 person-hour to complete 1 bridal centerpiece. How many of each type of arrangements should the florist produce daily for maximum profit, if the profit on a funeral wreath is $75and the profit on a bridal centerpiece is $40?

Solution :

Given

P = 75 x + 40 y

The constraints are

[tex]$x+y \leq 18$[/tex] .........(i) and          

[tex]$4x+y \leq 24$[/tex] .......(ii)

Solving (i) and (ii), we get

x = 2 and y = 16

Now

[tex]$x+y \leq 18$[/tex]   (total arrangement less than equal to 18)

[tex]$4x+y \leq 24$[/tex]   (total person hours less than equal to 24)

Maximum profit = 75 (2) + 40(16)

                          = 790

From the graph, the point of intersection and points that is plotted in between numbers between the 10 units on x-axis and y-axis are used in the graph.

So,

[tex]$x+y \leq 18$[/tex]  became [tex]$x+y \geq 18$[/tex]

[tex]$4x+y \leq 24$[/tex]   became  [tex]$4x+y \geq 24$[/tex]

[tex]$x \geq 0$[/tex]   became  [tex]$x \leq 0$[/tex]

[tex]$y \geq 0$[/tex]  became  [tex]$y \leq 0$[/tex]

So now the profit at point (0, 18) = 75(0)+40(18) = 720

Profit at point (6,0) = 75(6)+40(0) = 450

Profit at intersection point (2,16) = 75(2)+40(16)

                                                     = 150 + 640

                                                     = 790

Maximum profit = 790

So maximum profit is attained when 2 wreath are built and sold and 18 center pieces are built and sold.      

Define technological literacy.

The map shows rainfall amounts in the United States. A map of the United States shows where rain is currently falling and how heavy the rain is falling. Which presentation would most likely include this map? one that seeks to identify areas across the US that are prone to flooding one that analyzes global warming effects on the climate of the US one that seeks to show the many lakes and rivers in the US one that illustrates boundary lines between the states in the US