34. Suppose that an automobile manufacturer has accepted orders for 30 minivans, 25 sport utility vehicles, and 15 sedans. These orders can be represented by the row vector Q = [ 30 25 15 ]. The "raw materials" that go into each type of vehicle are steel, glass, plastic, paint, and labor. The entries in matrix R below give the number of units of each raw material (in this order) which are needed for each type of vehicle.
Suppose that steel costs $800 per unit, glass costs $400 per unit, plastic costs $300 per unit, paint costs $200 per unit, and
labor costs $1000 per unit. This data can be written as the column cost vector
The price the manufacturer negotiated for each minivan is $16,000, for each SUV is $21,000, and for each sedan is $13,000.
This information can be written as the column price vector
Find the amount of each raw material the manufacturer will need to fill the orders.