Algebra II h/w help

[Fire0nIce228 1]

This is the final problem on a 26 point homework assignment due tomorrow. Because of my extremely poor grade I need to do as best as possible. All the other problems on the homework, the values and inequalities are just given to you, but this one is a word problem. Here it is.

A biologist is developing two new strains of bacteria. Each sample of Type I bacteria produces 4 new viable bacteria, and each sample of Type II bacteria produces 3 new viable bacteria. Altogether, at least 240 new viable bacteria must be produced. At least 30, but not more than 60, of the orignal samples must be type I. Not more than 70 of the samples are to be type II. A sample of type I costs $5, and a sample of Type II costs $7. If both types are to be used, how many samples of each should be used to minimize the cost? Be sure to show all 7 steps used in solving this type of problem. (15 points)

I need to know.

The inequalities (so i can graph and shade them to make a feasable region)

and the function/ mathmatical problem I can use to find the maximum and minimum values.

It usually looks like this --- f(x,y)= mathmatical equation ( IE. x-2y)

so I can use that equation to plug in an x and y vertices from the points that make my shaded feasable region and get a numerical answer.

If anyone can help at all, even just getting the inequalities (less than, greater than, less than or equal to, greater than or equal to) so I can get the most points I can out of it. As in, she wont make me miss all 15 points if I atleast have some of it correct.

[Kovy_Ribs_Fedo 3]

1)

x:sample of Type I bacteria

y:sample of Type II bacteria

2)

x≥0

y≥0

3)

1- 4x+3y≥240

2- x+30≤60

3- y≤70

4) I couldn't put the graph here sorry, do it yourself with the three tops.

5)

Tops:

A(10, 70)

B(30, 70)

C(30, 40)

6)

Z= Ax + By

Z= 5x + 7y

7)----------------->Z= 5x+7y------------------->Results

A(10, 70)-------->Z= 5(10) + 7(70)--------->Z= 540$

B(30, 70)-------->Z= 5(30) + 7(70)--------->Z= 640$

C(30, 40)---------->Z = 5(30) + 7(40)--------->Z= 430$

8) 30 of sample I, and 40 of sample II.

[Kovy_Ribs_Fedo 3]

Hey Fireonice, I see you are not on MSH for the moment. I wish you will see my results before you leave for school tomorrow.

[Kovy_Ribs_Fedo 3]

SOLUTION EDITED

Yesterday I was tired and made a mistake on Inequalitie #1.

This my final, last and good solution.

Sorry, for the mistake...

On Inequalitie #1 : it's not x + y ≥240, it's 4x+3y≥240...