Acompany produces three combinations of mixed vegetables that sell in 1-kg packages. italian style combines 0.4 kg of zucchini, 0.3 kg of broccoli, and 0.3 kg of carrots. french style combines 0.5 kg of broccoli and 0.5 kg of carrots. oriental style combines 0.2 kg of zucchini, 0.3 kg of broccoli, and 0.5 kg of carrots. the company has a stock of 17 comma 800 kg of zucchini, 28 comma 300 kg of broccoli, and 38 comma 900 kg of carrots. how many packages of each style should it prepare to use up existing supplies?

Italian style = 18,000 packages

French style = 14,000 packages

Oriental style = 53,000 packages

Step-by-step explanation:

See the attached figure to represent the question

let the number of packages of Italian style = x

let the number of packages of French style = y

let the number of packages of Oriental style = z

By using the figure we can make the following equations:

0.4x + 0 * y + 0.2z = 17,800

0.3x + 0.5y + 0.3z = 28,300

0.3x + 0.5y + 0.5z = 38,900

Solving the 3 equations together to find x , y and z

Using the calculator:

x = 18,000 ⇒ Italian style packages

y = 14,000 ⇒ French style packages

z = 53,000 ⇒ Oriental style packages

0.0778

Step-by-step explanation:

Probability of false positive result, p = = 0.008

Sample size, n = 15,000

mean, μ = np = 15000 × 0.008 = 120

Now,

Standard deviation, σ =

or

=  

= 10.91

Now,

Probability of there being more than 135 false-positive results

= P(X > 135) ≈

or

= P(z > 1.42)

or

= 1 - P(z ≤ 1.42)

= 1 - 0.9222                 [P(z ≤ 1.42) = 0.9222 from standard z table]

= 0.0778

Hence,

P(X > 135) = 0.0778