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

.........(i) and          

.......(ii)

Solving (i) and (ii), we get

x = 2 and y = 16

Now

  (total arrangement less than equal to 18)

  (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,

 became

  became  

  became  

 became  

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.      

both are integral parts of a corporate balance sheet. the cash flow statement, or statement of cash flows, measures the sources of a company's cash and its uses of cash over a specific time period. the income statement measures a company's financial performance, such as revenues, expenses, profits or losses over a specific time period (in fact, it's sometimes called a statement of financial performance).

a cash flow statement shows exactly how much money a company has received and how much it has spent, traditionally over a period of one month. it captures the current operating results and changes on the balance sheet, such as increases or decreases in accounts receivable or accounts payable, and does not include noncash accounting items such as depreciation and amortization. the cash flow generally comes from revenue received as a result of business activity, but it may be augmented by funds available as a result of credit. a cash flow statement is used to determine the short-term viability and liquidity of a company, specifically how well it is positioned to pay its bills and vendors.