Based on bean et al. (1988). simon’s mall has 9000 square feet of space to rent and wants to determine the types of stores that should occupy the mall. the minimum number and maximum number of each type of store (along with the square footage of each type) are given in the file p06_74.xlsx. the annual profit made by each type of store depends on how many stores of that type are in the mall. this dependence is given in the same file. for example, if two department stores are in the mall, each department store will earn $210,000 profit per year. each store pays 7.5% of its annual profit as rent to simon’s. determine how simon can maximize its rental income from the mall.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

d. corresponding side lengths in similar triangles are proportional in length.

step-by-step explanation:

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: