Semester Project Group 6

 

Task# 1 : To find the slope between two points we have to use the slope formula.  

 

                A (4 , 10)   F (3.5, 7.5)

               We have to plug in the points into the slope formula.

 

                

 

                

 

                 

 

                To find the equation of the through the two points we plug in the slope and on of the point into

                 the point-slope formula. 

                

 

                 y-10=5(x-4)

                  y-10=5x-20

                  y=5x-10   slope-intercept form

 

                  -5x+y=-10 standard form

 

Task# 2 

 

               The inequality for task two would be 1400000 > 1000x+3000y

               The total amount of money we would get is 1400000 because we have $700 and we get $2000 per acre. The 1000x represents the amount of money per acre would get for cotton. The 3000y represents the amount of money per acre for pistachios.

 

 

Task# 3

                    The first inequality represents the amount of fertilizer needed compared to the amount available.

                    Fertilizer: 238000 > 300x + 400y

 

                   This second inequality represents the amount of water needed compared to the amount available.

                    Water: 1190 > 2x + 1y

 

Task# 4 

When farming cotton it cannot take up more than 80% so we came up with the equation

                    0 < x < 560.

                    For pistachios we cannot have it be more than 60% so we came up with the equation

                    0 < y < 420.

                    We came up with these equations by multiplying .6 and .8 times the amount of acres

                    we have. 

 

 

     

 

Task# 5          

                       We have to subtract the cost of producing from the selling price to determine our potential profit equation.

                        1500x + 4000y = Selling Price

                         1500x - 1000x + 4000y - 3000y = Profit

                          500x + 1000y = Profit

Our equation to determine potential profit is 500x + 1000y = P.

 

 

Task# 6          We have to plug in the vertices of our polygon in Task# 4 into our equation in Task# 5 to determine our maximum profit.The vertices of the polygon are points A, B, C, D, E, F, and G

 

                       500x + 1000y = P

 

                       Point A : 500(0) + 1000(420) = P

                                        0 + 420000 = P

                                           420000 = P

 

                       Point B : 500(140) + 1000(420) = P

                                              70000+420000 = P

                                                         490000 = P 

 

                       Point C : 500(308) + 1000(364) = P

                                            154000+364000 = P

                                                         518000 = P

 

                       Point D : 500(476) + 1000(238) = P

                                             238000+238000 = P

                                                        4760000 = P<<<<<<--------- the maximum profit!

 

                         Point E : 500(560) + 1000(70) = P           

                                            280000+70000  = P 

                                                        350000 = P

 

                       Point F : 500(560) + 1000(0) = P

                                                 280000+0 = P

                                                      280000= P   

 

                       Point G : 500(0) + 1000(0) = P                      

                                                         0 + 0 = P     

                                                               0 = P        

 

                          We determine that our maximum profit is $4760000.

 

Task# 7 

 

 

	glyphosate	%	gallons
54%	.54x	54%=.54	x
12%	.12(.38-x)	12%=.12	.38-x
Mixture	95.76	36%=.36	266

 

.54x + .12(.38-x) = 95.76

.54x + .0456-.12x = 95.76

.42x + .0456 = 95.76

.42x = 95.7144

x = 227.8914285...

 

 

 

 

Task# 8 

 

 

Dear Business Partners,

 

                    The information you have just read are the statisics and data that we have collected while farming our 700 acres. We have 300 acres of cotton and 400 acres of pistachios. Our profit equation would be 500x+1000y, x and y being cotton and pistachios. 238,000>300x+400y is the equation for the amount of fertilizer needed to the amount available. The equation for the amount of water needed compared to the amount available is 1190>2x+1y. The equation for the amount of cotton we are allowed to farm is 0<x< 560  and  0<y<420 is the equation for the amount of pistachios we are allowed to farm. Hopefully our land is what you are looking for! Thank You.