Formulate and solve on spreadsheet and please be in details, if possible provide

Question

Formulate and solve on spreadsheet and please be in details, if possible provide screen shots.

Bravura cosmetics (BC) produces kaya rose perfume, which requires chemicals and labor. Two production process are available. Process 1 transforms 1 unit of labor and 2 units of chemicals into 3 ounces of perfume. Process 2 transforms 2 units of labor and 3 units of chemicals into 5 ounces of perfume. It costs BC $3 to purchase a unit of labor and 35,000 units of chemicals. Each year upto 20,000 units of labor and 35,000 units of chemicals can be purchased . In the absence of advertising, BC believes it can sell 1000 ounces of perfume. To stimulate demand for kaya rose, BC can hire the lovely model harriet hauch. Harriet is paid $100 per hour. Each hour harriet works for the company is estimated to increase the demand for kaya rose perfume by 200 ounces. Each ounce of kaya rose perfume sells for $5.

Determine how BC can maximize its profit.

Explanation / Answer

Answer:

x1 => units of process 1

x2 => units of process 2

x3 => modeling hours

Maximize z=5*(3*x1+5*x2) -3*(x1+2*x2) -2*(2*x1+3*x2) -100*x3

Subject to the constraints x1+2*x2<=20000 (Limited labor)

2*x1+3*x2<=35000 (Limited chemicals)

3*x1+5*x2=1000+200*x3

After modifying the constraints:

z=8*x1+13*x2-100*x3

x1+2*x2<=20000

2*x1+3*x2<=35000

3*x1+5*x2-200*x3<=1000

-3*x1-5*x2+200*x3<= -1000

Then set up the initial table:

Since there is a negative entry(-1000) in RHS column Phase I applies

Now there remained no negative number in the RHS column, so Phase II applies from now on

Pivoting process is applied one more time in order to make the negative entry of the objective function positive and obtain the optimum value of z. The final table is:

The maximum profit is z= $118000.

Table :a Bv P x1 x2 x3 s1 s2 s3 S4 RHS P 1 -8 -13 100 0 0 0 0 0 S1 0 1 2 0 1 0 0 0 20000 S2 0 2 3 0 0 1 0 0 35000 S3 0 -3 -5 200 0 0 1 0 -1000 S4 0 3 5 -200 0 0 0 1 1000

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