- anonymous

the ace novelty company wishes to produce two types of souvenirs: type A and type B. to manufacture a type A souvenir requires 2 minutes on machine 1 and 1 minute on machine 2. a type B souvenir requires 1 minute on machine 1 and 3 minutes on machine 2. There are 180 minutes available on machine 1 and 300 minutes available on machine 2 for processing the order. let x represent the number f type A souvenirs produced and let y represent the number of type B souvenirs produced
a. Write linear equalities that give appropriate restrictions on x and y
b. If each type A souvenir will result in a prof

- jamiebookeater

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- anonymous

b. if each type a souvenir will result in a profit of $1 and each type b souvenir will result a profit of 1.20 then express the profit, p in terms of x and y.
c. algebraically determine how many souvenirs of each type the ace novelty company should produce so as to maximize profit

- amistre64

The ace novelty company wishes to produce two types of souvenirs: type A and type B.
To manufacture type A requires:
2 minutes on machine 1
1 minute on machine 2
Type B requires:
1 minute on machine 1
3 minutes on machine 2
There are
180 minutes available on machine 1
and 300 minutes available on machine 2
for processing the order.
Let x =# of type A produced
Let y = # of type B produced

- amistre64

a) Write linear equalities that give appropriate restrictions on x and y.
What ype of restrictions? cant seem to understand the question yet

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## More answers

- anonymous

i think we have time restrictions
2x+y<=180
and x+3y<=300

- amistre64

f = first machine; s = second machine
A = 2f + s
B = f + 3s

- anonymous

p=x+1.2y

- anonymous

yes then my teacher evaluates and gets y≤-2x and y≤ 200-x/3

- amistre64

are the machines breaking down after so many minutes?

- anonymous

thats 180-2x

- anonymous

yes when i typed y≤-2x it was supposed to be y≤180-2x

- anonymous

not sure where he got those answers

- anonymous

for each x type you spend 2 minutes on machine one. for each y type you spend 1 minute on machine one. the total time on machine 1 is 2x+y and it must be less than or equal to the total time of machine 1 which is 180. thats where the equations come from

- anonymous

to maximimze profit graph the region and find the maximum of p=x+1.2y on the boundaries.

- anonymous

does the two in 2x stand for the umber of minutes?

- anonymous

number

- anonymous

yes two minutes per part * x number of parts

- anonymous

how would i find the p=x+1.2y by using the calculator?

- anonymous

do you know how to find maximums of functions?

- anonymous

with cornerpoints

- anonymous

you plug in the boundary for y in the p=x+1.2y term and you find its maximum on both boundaries. The highest of the two maxes is your max profit.

- anonymous

you should draw the region first and find the intersection

- anonymous

there are four different cornerpoints according to the sheet

- anonymous

yeah there are. one of them is 0,0 which you can rule out right away. then check the other 3 points and choose the largest

- anonymous

can you explain how to find the others?

- anonymous

sure. you have two inequalities for y. do you know how to graph them?

- anonymous

y<=180-2x
y<=100-x/3

- anonymous

i put them into my y= and then have the calculator shade

- anonymous

it didn't work right for me

- anonymous

try drawing it by hand on paper. The first has y intercept 180 and slope -2 the second has y intercept 100 slope -1/3

- anonymous

y=180-2x has y intercept 180 x intercept 90.
y=100-x/3 has y intercept 100 x intercept 300

- anonymous

then y has to be less than both of those lines. So the cornerpoints are (0,0), (0,100), (90,0), (240/7,620/7). plug them into the profit equation and see which is the highest.

- anonymous

the 4th cornerpoint is the intersection of the two lines

- anonymous

woops the intersection point is (48,132) actually

- anonymous

it is the maximum still

- anonymous

jeez sorry (48,84)

- anonymous

(48,84)=(x,y) p=148.8 is the final answer

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