Suppose you are in the business of manufacturing white board markers. You make two types: Standard and Heavy Duty. You sell these to wholesalers for $10/box of 10 for Standard Markers and $15/box of 10 for Heavy Duty markers. Each standard marker is made up of 3 oz. of plastic and 1 fl. Oz. of marker fluid. Each Standard Marker is made up of 5 oz. of plastic and 1.5 fl. oz of marker fluid. Plastic costs $1/lb and marker fluid costs $5/gal. Each marker takes 30 seconds to manufacture by machine, but the machine can manufacture up to 10 at one time. Machine time costs $60/hr.

Set up the profit function for each type of marker, using dimensional analysis as you would have to do for a linear program objective function where you wanted to maximize profit.

Multiple answers

Step-by-step explanation:

Let change the name of the variables.

Set Standard as X and Heavy Duty as Y

The X markers costs 10/box with 10 markers = $1 per maker.

The Y markers costs 15/box with 10 markers = $1.5 per marker.

The X marker is made of 3 oz. of plastic and 1fl. oz of marker fluid.

The Y marker is made of 5 oz. of plastic and 1.5fl. oz. of marker fluid.

Plastic cost $1/lb and marker fluid costs $5/gal.

1 oz = .0625lb

1 fl. oz. = 0.0078125gal

∴

Once we have the cost per marker:

The machine time cost is of $60/hr but each marker takes 30 seconds to be manufactured.

So we divide 1 hr / 30s and multiply it by the 10 markers the machine can produce at one time.

One hour of machine time costs $60. We divide the cost of machine time by the total markers can be produced in one hour.  

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional