I need help with this math problem?

Question

A manufacturer purchases a part for use at both of its plants-one at Roseville, CA, the other at Akron, OH. The part is available in limited quantities from two suppliers. Each supplier has 75 units available. The Roseville plant needs 35 units, and the Akron plant requires 75 units. The first supplier charges $70 per unit delivered to Roseville and $90 per unit delivered to Akron. Corresponding costs from the second supplier are $80 and $120. The manufacturer wants to order a total of 75 units from the first, less expensive, supplier, with the remaining 35 units to come from the second supplier. If the company spends $9750 to purchase the required number of units for the two plants, find the number of units that should be purchased from each supplier for each plant.

P.S. please show the necesarry setup needed to solve this problem.

Answer 1

As first supplier is less expensive 75 units will be purchased from him
let x units for Akron plant at the rate of $ 90 and y units for Roseville at the rate of $70
x + y =75 ---- eqn (1)
Cost towards first supplier
90x + 70 y ----- eqn (2)
From second supplier (75 -x) units for Akron plant at the rate of $120 and (35 - y) units for Rosville at the rate of $ 80
cost towards second supplier
(75-x)120 + (35 - y)80 =
9000 - 120x + 2800 - 80y =
11800 - 120x -80 y ---- eqn (3)
Total expenditure, eqn (2) + eqn (3) = 9750
90x + 70y + 11800 -120x -80 y = 9750
rearranging
-30x -10y = 9750 - 11800
-30x - 10y = -2050
dividing by -10
3x + y = 205 ---- eqn (4)
x + y =75 ----- eqn (1)
subtracting eqn(1) from eqn (4)
2x = 130
x = 65
substituting x value in eqn (1)
65 + y =75
y = 10
From first supplier
65 units for for Akron at the rate of $90 and
10 units for Roseville at the rate of $70
From second supplier
10 units for Akron plant at the rate of $120 and 25 units for Roseville at the rate of $80

Answer 2

So 75 units are shipped to Akron at a cost 90$ per unit so total is 90*75 = $6750.
Then 35 units at $80 per unit are shipped to Roseville at a cost of 35*80 = $2800.
Total cost is 6750+2800 = $9550.
So manufacturer paid $200 too much.

Answer 3

ns1 = number from supplier 1 for roseville = 10
ns2 = number from supplier 2 for roseville = 25

number from supplier 1 for akron = 75 - 10 =65
number from supplier 2 for akron = 35 - 25 = 10

Working:
Let us call the number of parts from supplier 1 to roseville as ns1. Let us call the number of parts from supplier 2 to roseville as ns2. Using these 2 variables, we can derive 3 linear equations of which 2 will suffice. I chose these 2.

equation1 :
ns1*70 + (75-ns1)*90 + ns2*80 + (35-ns2)*120 = 9750

equation 2:
ns1+ns2 = 35

If you reduce equation 1 to its simplest form it will become
ns1+2ns2=60

So if you solve this equation and equation 2, you will get the values for ns1 and ns2. (shown above),