a home security company plans to open a calling center to respond to customer calls and emails. they plan to buy a large building with one large room to place cubicles where operators will work. there are two options for cubicles: small cubicles for one operator that is 49 square feet and larger cubicles for two operators that is 80 square feet. the company knows it wants a minimum of 12 cubicles, but because of the expense of additional employees, they want a maximum of 20 operators.

write a system of inequalities to model the calling center that would the company determine the number of cubicles to build and the number of operators to be employed. define any variables used.

t hope this

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step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt