Shelf Assembly

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algebra 2 math help plz im desperate ?

ok i can do my own hw but i am in serious need of help ive been working on this prob for 2 hrs w/ a tutor and i still dont get it!
plzzzzz help me

Surehold shelving company produces 2 types of decorative shelves. the old english style takes 20 mins to assemble and 10 mins to finish. the cool contemporary style takes 10 minutes to assemble and 20 minutes to finish. each day there are 48 hours of work in the assembly department and 64 hrs of work in the finishing dept. the company must make at least 200 shelves each day. cost for old english shelf=$2.00 cost for contempory is $2.50.
how many of each type of shelf should the company produce to minimize the cost of materials and still meet its production commitments (200 shelves)?

help much appreciated plz show work(i wont copy i am just xtremely frustrated and want to know the answer)

fyi our teacher just wants us to make an effort (done already)

thx ;D

Let "x" be the fraction of Olde English (OE) shelves. (1-x) would be the fraction of Cool Contemporary (CC). Since the cost of CC is higher, you want to make as many OE as possible, within labor constraints. This problem is labor constrained in the assembly department.

The assembly labor is:

(200)*x*20/60 + (200)*(1-x)*10/60 = 48hours

(200/3)x - (200/6)x = 48 - 200/6
(200/6)x = (48 - 200/6)
x = (6/200)*(48-200/6) = 0.44

You cannot make more than 44% OE, or you run out of assembly labor, and wouldn't make the 200 unit commitment.

If you check the labor loading in finishing, the fraction is higher, so the assembly department is the dominating constraint. The Finishing department labor calculation is:

(200)*x*(10/60) + (200)*(1-x)*(20/60) = 64 hours.

(200/6)*x - (200/3)*x = 64 - 200/3
(-200/6)*x = 64 - 200/3
x = (-6/200)*(64 - 200/3) = 0.80 or 80% OE

Since the labor demand is different between the two styles, we need to verify that we have enough finishing labor to accommodate the assembly limited mix.

.44*200 = 88 OE

200 - 88 = 112 CC

(88*10 + 112*20)/60 = 52hours finishing

So, you have more than enough finishing labor to complete all of the units that assembly can produce. Probably you should consider retraining some of the finishing labor for the assembly department.

So, you would make 88 OE, and 112 CC.

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Shelfsave Boltless Shelving Assembly.avi