Question

Quickbrush Paint Company is developing a linear program to determine the optimal quantities of ingredient A and ingredient B to blend together to make oil-based and water-based paint. The oil-based paint contains 90 percent A and 10 percent B, whereas the water-based paint contains 30 percent A and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of ingredient B in inventory and cannot obtain more at this time. Assuming that x represents the number of gallons of oil-based paint, and y represents the gallons of water-based paint, which of the following constraint correctly represents the constraint on ingredient A?

a. 0.9x + 0.3y ≤ 10,000
b. 0.9A + 0.1B ≤ 10,000
c. 0.9x + 0.1y ≤ 10,000
d. 0.3x + .7y ≤ 10,000

Answer 1

Constraint A is represented by 0.9x + 0.3y ≤ 10,000

Step-by-step explanation:

Linear programming is a mathematical model that is used to solve a problem when a firm wants to maximize profit in the midst of multiple resource constraints.

The following steps should be followed:

Step 1: Define the variables

x= the gallons of oil-based paint

y= the gallons of water-based paint

Step 2: Define the constraints:

The constraints represent the limitations which could be resource; in this case ingredients A and B. Since the constraint in focus is A, so we only consider A

Constraint A = 0.9x + 0.3y ≤ 10,000

Non-negativity constraints x, y ≥ 0

Since the total inventory amount of ingredient A available is 10,000 gallons then the total consumption can either be equal to or less than 10,000, but can never be higher than 10,000

Constraint A is represented by 0.9x + 0.3y ≤ 10,000