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