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.

Question

Mathematics

Axel Hood

7 September, 12:59

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.

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Answers (1)

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Damian Winters · Answer 1

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

∴

$X = 3 (.0625lb) * $1 (the cost of the plastic in the marker) + 1 (0.0078125gal) * $5 (the cost of the marker fluid in the marker) =.1875 +.0390625 =.2265625 (the total cost of the X marker). $Y = 5 (.0625lb) * $1 (the cost of the plastic in the marker) + 1.5 (0.0078125gal) * $5 (the cost of the marker fluid in the marker) =.3125 +.05859375 =.37109375 (the total cost of the Y marker).

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.

(3,600 s / 30s) * 10 = 1200 (the total of markers the machine can produce per hour)

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

$60/1200=$.05 (this is the cost of manufactured per marker).