Use ip to formulate and solve the following problem: a chain of stores has too many stores in close proximity. specifically, the store numbers within each grouping are too close: (1,3), (1,2,4), (4,5,6), (6,9), (6,7,8), (8,10), (9,10). it only wishes to retain 7 stores, one within each of these groupings. the monthly profit from each store is given. the objective is to select the stores to retain to maximize overall profits. the profits of the stores are 12,15,18,10,9,18,12,13,11, and 8.

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step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.