formulate linear equations: A company produces two types of juices: orange & pineappl

[unkownhesoka]

formulate linear equations: A company produces two types of juices: orange & pineappl

i have struggled with this problem for 2 hours now -.-

A company produces two types of juices: orange juice and pineapple juice. The preparation of the products requires cleaning, filling and labeling bottles.

Each case of orange juice requires 10 minutes in the cleaning machine, 4 minutes in the filling machine, and 2 minutes in the labeling machine. Each case of pineapple juice requires 8 minutes in the cleaning machine, 6 minutes in the filling machine, and 1 minute in the labeling machine.

The company decided to run the cleaning machine for 6 hours, the filling machine for 4 hours, and the labeling machine for 2 hours. Moreover, in order to meet the demand, the company is required to produce 200 cases of orange juice and 150 cases of pineapple juice.

It is required to determine the number of cases of each type of juice that should be produced.
(Formulate only the system of linear equations)

 

[stapel]

i have struggled with this problem for 2 hours now -.-

Then you've got loads of work that you can show us. Excellent!

A company produces two types of juices: orange juice and pineapple juice. The preparation of the products requires cleaning, filling and labeling bottles.

Each case of orange juice requires 10 minutes in the cleaning machine, 4 minutes in the filling machine, and 2 minutes in the labeling machine. Each case of pineapple juice requires 8 minutes in the cleaning machine, 6 minutes in the filling machine, and 1 minute in the labeling machine.

The company decided to run the cleaning machine for 6 hours, the filling machine for 4 hours, and the labeling machine for 2 hours. Moreover, in order to meet the demand, the company is required to produce 200 cases of orange juice and 150 cases of pineapple juice.

It is required to determine the number of cases of each type of juice that should be produced.
(Formulate only the system of linear equations)

You are told the unknowns that you are supposed to find: the numbers of cases of each type of juice. So what variables have you picked for these unknowns? (Note: I am assuming that the "in order to meet the demand" numbers are minimums, rather than fixed amounts; otherwise, the exercise makes no sense.)

You are given values for the amount of time needed in the cleaning machine, given the (currently unknown) numbers of cases. What expression did you create with this information?

You are given a total time for the cleaning machine. What equation did you create with this information and the expression from above?

You are given values, in a similar manner, for the filling and labeling machines. What equations did you create with these facts?

Please be complete. Thank you!

 

[unkownhesoka]

Then you've got loads of work that you can show us. Excellent!

will nothing much but i ended up at this

i assumed that x= numbers of cases of orange juice Y= number of cases of pineapple juice

10x+8y=360
4x+6y=240
2x+y=120

Converting total machine hours of work to min (6*60, 4*60, 2*60)

but i find my self not including the the total cases required by the company which is 200 cases of orange and 150 of pineapple

 

[unkownhesoka]

Then you've got loads of work that you can show us. Excellent!


You are told the unknowns that you are supposed to find: the numbers of cases of each type of juice. So what variables have you picked for these unknowns? (Note: I am assuming that the "in order to meet the demand" numbers are minimums, rather than fixed amounts; otherwise, the exercise makes no sense.)

You are given values for the amount of time needed in the cleaning machine, given the (currently unknown) numbers of cases. What expression did you create with this information?

You are given a total time for the cleaning machine. What equation did you create with this information and the expression from above?

You are given values, in a similar manner, for the filling and labeling machines. What equations did you create with these facts?

Please be complete. Thank you!

one of the equation should be like this the time each type need to finish for X (orange ) need's 16 min to finish the other Y ( Pineapple ) need's 15 min to finish
the equation is ( 16 X + 15 Y = 720 )
and 720 min is the total machine running time ( 6 H + 4 H + 2 H ) = 12 H * 60 = 720 min