Question

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

Answer 1

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

Answer 2

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

Answer 3

a) Write linear equalities that give appropriate restrictions on x and y.

What ype of restrictions? cant seem to understand the question yet

Answer 4

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

Answer 5

f = first machine; s = second machine

A = 2f + s

B = f + 3s

Answer 6

p=x+1.2y

Answer 7

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

Answer 8

are the machines breaking down after so many minutes?

Answer 9

thats 180-2x

Answer 10

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

Answer 11

not sure where he got those answers

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

number

Answer 16

yes two minutes per part * x number of parts

Answer 17

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

Answer 18

do you know how to find maximums of functions?

Answer 19

with cornerpoints

Answer 20

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.

Answer 21

you should draw the region first and find the intersection

Answer 22

there are four different cornerpoints according to the sheet

Answer 23

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

Answer 24

can you explain how to find the others?

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

it didn't work right for me

Answer 29

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

Answer 30

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

Answer 31

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.

Answer 32

the 4th cornerpoint is the intersection of the two lines

Answer 33

woops the intersection point is (48,132) actually

Answer 34

it is the maximum still

Answer 35

jeez sorry (48,84)

Answer 36

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