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Year 11 Maths Methods SAC ANALYSIS TASK

The UP-IT Company

UP-IT, a small home-based company manufacturing star-picket-pullers for removing star-pickets from old fences, has fixed operating costs of $15,000 per year. In addition to these fixed costs, it costs $8 to manufacture each star-picket-puller.

1. To determine the total cost, $C, for manufacturing star-picket-pullers per year you would have to times the number of star-picket-pullers, s, by $8 and then add the fixed operating cost of $15,000.

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$C= 8s + 15,000

. i. If the annual production is 00 star-picket-pullers, to find the overall annual cost, $C, you would have to times the number of star-picket-pullers manufactured, 00, by the cost of manufacture, $8, and then add the fixed operating cost of $15,000. After doing all that you should get $,400 as your overall annual cost, $C.

$C=8(00) + 15,000

=,400

ii. If the annual production is 00 star-picket-pullers, to find the overall cost per star-picket-puller, $/spp, you have to get the overall annual cost, ,400, and then divide by the number of star-picket-pullers manufactured, 00. After doing all that you should get a cost of $78 per star-picket-puller.

$/spp=,400

00

=78

. For the overall cost per star-picket-puller to be $58 they would have to manufacture 500 star-picket-pullers. With the production of 500 star-picket-pullers the overall annual cost would be $,000. Divide that by the number made which was 500 and you end up with $58 per star-picket-puller.

$58=8s +15,000

s

$58s=8s + 15,000

$0s=15,000

s=500

4. To get the total cost, $T, per star-picket-puller you have to times the number of star-picket-pullers manufactured, s, by $8 then add the fixed operating cost of $15,000 then divide by the number manufactured, s.

$T=8s + 15,000

s

5. If UP-IT sells star-picket-pullers for $110 each their income, $I, would be 110 times the number of star-picket-pullers sold, s.

$I=110s

7. To determine how many star-picket-pullers must be sold in order to make a profit first you must determine how much money is being made from each sale of a star-picket-puller by subtracting the cost, $8, from the income, $110, to get the profit per star-picket-puller, $P/spp. Then divide the fixed operating cost by the profit per star-picket-puller. Round the number up and the number you get is how many star-picket-pullers needed to ‘break even’.

$P/spp=110 - 8

=8

=15,000

8

=18.

=18

8. To determine the profit, $P, you have to subtract the cost, $C, which is 8 times the number manufactued, s, plus the fixed operating cost of $15,000 from the income, $I, which is 110 times the number manufactured, s.

$P=110s � (8s + 15,000)

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