A supply company manufactures masks and ventilators for hospitals. To maintain hugh quality, the company should not manufacture more than a total of 120 masks and ventilators per day. To meet customer demand, the company must manufacture between 10 and 50 masks per day, inclusive. The company must manufacture at least 40 and no more than 100 ventilators per day. The company's profits are $10 per mask and $65 per ventilator

20 masks and 100 ventilators

Step-by-step explanation:

I assume the problem ask to maximize the profit of the company.

Let's define the following variables

v: ventilator

m: mask

Restictions:

m + v ≤ 120

10 ≤ m ≤ 50

40 ≤ v ≤ 100

Profit function:

P = 10*m + 65*v

The system of restrictions can be seen in the figure attached. The five points marked are the vertices of the feasible region (the solution is one of these points). Replacing them in the profit function:

point          Profit function:

(10, 100)    10*10 + 65*100 = 6600

(20, 100)    10*20 + 65*100 = 6700    

(50, 70)      10*50 + 65*70 =  5050

(50, 40)     10*50 + 65*40 = 3100

(10, 40)      10*10 + 65*40 =  2700

Then, the profit maximization is obtained when 20 masks and 100 ventilators are produced.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8