A pharmaceutical company produces three kinds of cold formulas: A, B, and C. it takes 1.5 hours to produce 1000 bottles of the Formula A, 2 hours to produce 1000 bottles of formula B. and 3 hours to produce 1000 n=bottles of formula C. The profits for each 1000 of Formula A, formula B, and Formula C is $100, $150, and $210, respectively. Suppose that for a certain production run. There are enough ingredients on hand to make at most 7000 bottles of formula A, 14000 of formula B, and 3000 bottles of formula C. Furthermore, suppose the time for the production run is limited to a maximum of 50 hours. They want to maximize their profit, P. in dollars. Which of the following is the correct objective function? a. z= 100.11 + 150.x2 + 210x3
b. z =1000x1 + 1000x2 + 1000x3
c. z=700.01 + 14000x2 + 3000x3
d. z= 1.5x1+ 2x2 + 3x3

z = 100*x₁  + 150*x₂  +  210*x₃

Step-by-step explanation:

Lyric a looks like there is a typing error in the first term ( 100.11 ) .

the right is 100*x₁

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)