I need help with the following 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 matrixes needed to setup and solve this problem.

Answer 1

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. Therefore the manufacturer orders 75 units from the ist supplier at $90 per unit and ships them to Akron. This costs 90*75 = $6750. Now the 2nd supplier ships 35 units to Roseville at $80 per unit for a cost of 80*35 = $2800. Total cost is 6750+2800 = $9550. This is all forced by the first sentence of my answer which is a condition you imposed in your question. The company payed $200 more than they should have and should demand a refund. No matrices are necessary to solve this problem.

I have a feeling you have not properly stated the problem.