Acandy manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock. he decides to sell them in the form of two different mixtures. one mixture will contain half cherries and half mints by weight and will sell for $2.00 per pound. the other mixture will contain one-third cherries and two-thirds mints by weight and will sell for $1.25 per pound. how many pounds of each mixture should the candy manufacturer prepare in order to maximize his sales revenue?

He should prepare 260 pounds of first mixture and 0 pounds of second mixture

Step-by-step explanation:

Let x be the total quantity ( in pounds ) of cherries and mints in the first mixture and y be the total quantity in second mixture,

Since, first mixture will contain half cherries and half mints by weight,

That is, in first mixture,

Cherries =

Mints = ,

While, second mixture will contain one-third cherries and two-thirds mints by weight,

That is, in second mixture,

Cherries =

Mints =

According to the question,

The manufacturer has 130 pounds of chocolate-covered cherries and 170 pounds of chocolate-covered mints in stock,

That is,

Also, pounds can not be negative,

x ≥ 0, y ≥ 0,

Since, the first and second mixture must be sell at the rate of $2.00 per pound and $1.25 per pound respectively,

Hence, the total revenue,

Z = 2.00x + 1.25y

Which is the function that have to maximise,

By plotting the above inequalities,

Vertex of feasible regions are,

(0,255), (180, 120) and (260, 0),

Also, at (260, 0), Z is maximum,

Hence, he should prepare 260 pounds of first mixture and 0 pounds of second mixture in order to maximize his sales revenue.

use substitution to solve each system of equations. y = x + 5 3x + y = 25 62/87,21 y = x + 5 3x + y = 25 substitute x + 5 for y in the second equation. substitute the solution for x into either equation to find y. the solution is (5, 10)

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step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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