Given the following: zA = 20 - 3x zB = 18 - 2y, where z is marginal utility per dollar spent, x is the amount spent on product A, and y is the amount spent on product B. Assume that the consumer has $14 to spend on A and B—that is: x + y = $14.

Instructions: Enter your answers as whole numbers.

a. How is the $14 best allocated between A and B?

$ on A.

$ on B.

b. How much utility will the marginal dollar yield? utils.

a. x= $6, y= $8

b. z= $2

Step-by-step explanation:

at equilibrium, the marginal utility per dollar spent will be equal i.e

zA=zB

20-3x=18-2y

upon simplification, we arrive at

......equation 1

since the total amount to spend is $14, then

x+y=14

x=14-y..............equation 2

if we solve equation 1 and equation 2 simultaneously

Hence for y=8

x=14-y=14-8

x=6

Hence the amount spent on Product A is $6 and the amount spent on product B is $8

b. to determine the amount of utility the marginal dollar will yield, we substitute the values of y and x into the the given equation,

zA=20-3x=20-3(6)

zA=20-18=2

zB=18-2y=18-2(8)

zB=18-16=2

hence the amount spent on the marginal utility is $2

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the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet