Plz! help me wit this!! im cryin cuz i cant git it...plz help me :[?

Sports on Wheels produces skateboards and roller blades. Producing a skateboard requires 4 hours on machine A and 2 hours on machine B. Producing a pair of roller blades requires 6 hours on machine A, 6 hours on machine B, and 1 hour on machine C. Machine A is available 120 hours per week, macine B is available 72 hours per week, and machine C is available 10 hours per week. If the company profits $33 on each skateboard and $22 on each pair of roller blades, how many of each should be produced to maximize the company%26#039;s profit?

Plz! help me wit this!! im cryin cuz i cant git it...plz help me :[?
wtf. Take a wild guess...Everyone does it (especially me)
Reply:you should be running a program like LINDO to figure this out...but heres my go at it:





a-120 max


b-72 max


c-10 max





skateboard= 4a+2b


rollerblades=6a+6b+1c





constraints--


skateboard:


a%26lt;=120


b%26lt;=72








rollerblades:


a%26lt;=120


b%26lt;=72


c%26lt;=10








profit:


4a+2b=33


6a+6b+1c=22





so you want to maximize


4a+2b=33 and 6a+6b+1c=22
Reply:I%26#039;m not sure... but this is the way I worked it out:





You can only produce 10 roller blades a week because machine C is only available 10 hrs a week and you need 1 hour for each set of roller blades.





So since you%26#039;re doing 10 roller blades you%26#039;ll be using machine A 60 hrs a week, and machine B 60 hrs a week.





Now you have 60 hours left on machine A to make skateboards, and you have 12 hours on machine B.





You need 2 hours on machine B to make each skateboard, so you can only use it 6 times.





You%26#039;ll be producing 10 roller blades and 6 skateboards a week.





Although, now that I worked it out that way... I don%26#039;t think that maximizes the company%26#039;s profits.
Reply:Ok, first express the problem mathmatically





Skateboards = 4a + 2b (hrs per machine to make a product)


Rollerblades = 6a + 6b + c





So if the Max # of hours is 120 for a, 72 for b, and 10 for c, find:





For the number of hours availiable on each machine, how many could be produced max;





since it takes 4 hrs to make a skateboard on a, divide 120 by 4, giving you 30 max skateboards for the number left on a.





Doing the same for machine b, you find that 36 is the maximum number of skateboards for THAT machine,


so total there can only be 30 or less skateboads, since machine a and b are needed.





----Now do this same process for rollerblades.





a = 20 max, b= 12 max, c =10 max





So there can only be a maximum of 10 rollerblades made per week.





(Now keep in mind, skateboards are worth more)---- so if 30 skateboards are produced, this leaves 12 b hrs left over and zero a hrs. (Inefficient)





So if there are 12b hrs, this can produce 2 sets of rollerblades, meaning you also need 12 a hrs, and 2 c hrs.








120a-12a= 108a 108a divided by 4a (# required for skateboards) gives you 27Skateboards.





27 Skateboards would use 108a, 54 b and 0c





So there are 12 a left, 18b and 10 c leftover after 27 Skate boards.





Now you can make 2 rollerblades with the remaining hours leaving leftover hrs of 0a, 6b, and 8c.





27skateboards x $33= $891


2 Rollerblades x $22= $44


Giving you a total of $935



sweating