A company manufacturers two types of paint called A and B. With each barrel of A

Question

A company manufacturers two types of paint called A and B.
With each barrel of A that they produce they earn a profit of $11 and with each barrel of B that they produce they earn a profit of $20.
Each type of paint must first go through a blending station and then a mixing station and finally an inspection station.
For each barrel of Product A produced twenty-two minutes are required in the blending station, twelve minutes are required in the mixing station and ten minutes are required in the inspection station.
For each barrel of Product B produced fourteen minutes are required in the blending station, sixteen minutes are required in the mixing station and twenty-five minutes are required in the inspection station.
On any given twenty-four hour day in which the operation runs, there are 3080 man-minutes available in blending, 1920 man-minutes available in mixing and 2500 man-minutes available in inspection.

A couple of other factors that might need to be taken into consideration are these:

In any given twenty-four hour day, only 217 barrels are available so the total number of barrels produced cannot exceed this amount;

Because of union rules at least 25 barrels of each type must be produced each day;

If the optimal quantities are not whole numbers of barrels, it's okay and it should be reported as such in the MEMO, but round to two decimal place accuracy;

The optimal profit should be rounded to the nearest penny.

How many barrels of each type of paint should they produce in order to maximize their profit?
what is that profit?
How many man-minutes are left over in each department?
how many barrels are left over?

Explanation / Answer

stages minits taken minits taken minits taken time paint A paint paint B avail blending 22 14 3080 mixing 12 16 1920 inspect 10 25 2500 total 44 55 7500 profit 11 20 % 25% 36.36% From the above table the paint "B" is giving high profit rather than paint "A" So the optimum mix should be give less priarity to make Paint "A" the constraints here 1.the production of barriers should not exceed 217 barrels 2.min requiremnt from each paint is 25 barrels so from the above table fo 1 barrel of paint "A" is taking 44 mins for 25 barrel = 25*44 =1100 mins remain all goes for mking of paint "B" to maxmize the profit. How many barrels of each type of paint should they produce in order to maximize their profit?
paint A = 1100/44 = 25 barrels paint B = [7500-1100]/55=116.36 barrels(aprox 116) so the total barrels = 25+116 = 141 barrels paint A = 1100/44 = 25 barrels paint B = [7500-1100]/55=116.36 barrels(aprox 116) so the total barrels = 25+116 = 141 barrels
what is that profit? paint A = 25 *11 = $275 paint B = 116*20= $2320 toal profit would be =2320+275=$2595 how many barrels are left over? the scope of barrels to made = 217 actual posibitiy = 25+116 = 141 leftover = [217-141] = 76 barrels               
stages minits taken minits taken time paint A paint B avail blending 22 14 3080 mixing 12 16 1920 inspect 10 25 2500 total 44 55 7500 profit 11 20 % 25% 36.36%

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