anonymous
  • 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
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • 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
  • 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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anonymous
  • anonymous
i think we have time restrictions 2x+y<=180 and x+3y<=300
amistre64
  • amistre64
f = first machine; s = second machine A = 2f + s B = f + 3s
anonymous
  • anonymous
p=x+1.2y
anonymous
  • anonymous
yes then my teacher evaluates and gets y≤-2x and y≤ 200-x/3
amistre64
  • amistre64
are the machines breaking down after so many minutes?
anonymous
  • anonymous
thats 180-2x
anonymous
  • anonymous
yes when i typed y≤-2x it was supposed to be y≤180-2x
anonymous
  • anonymous
not sure where he got those answers
anonymous
  • 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
  • anonymous
to maximimze profit graph the region and find the maximum of p=x+1.2y on the boundaries.
anonymous
  • anonymous
does the two in 2x stand for the umber of minutes?
anonymous
  • anonymous
number
anonymous
  • anonymous
yes two minutes per part * x number of parts
anonymous
  • anonymous
how would i find the p=x+1.2y by using the calculator?
anonymous
  • anonymous
do you know how to find maximums of functions?
anonymous
  • anonymous
with cornerpoints
anonymous
  • 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
  • anonymous
you should draw the region first and find the intersection
anonymous
  • anonymous
there are four different cornerpoints according to the sheet
anonymous
  • 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
  • anonymous
can you explain how to find the others?
anonymous
  • anonymous
sure. you have two inequalities for y. do you know how to graph them?
anonymous
  • anonymous
y<=180-2x y<=100-x/3
anonymous
  • anonymous
i put them into my y= and then have the calculator shade
anonymous
  • anonymous
it didn't work right for me
anonymous
  • 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
  • anonymous
y=180-2x has y intercept 180 x intercept 90. y=100-x/3 has y intercept 100 x intercept 300
anonymous
  • 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
  • anonymous
the 4th cornerpoint is the intersection of the two lines
anonymous
  • anonymous
woops the intersection point is (48,132) actually
anonymous
  • anonymous
it is the maximum still
anonymous
  • anonymous
jeez sorry (48,84)
anonymous
  • anonymous
(48,84)=(x,y) p=148.8 is the final answer

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