thank you for helping me last night. I have some more problems that involve "solver". I have attached theanswer. can you please putit in excel solver. thank you

question: a plumbing manufacturer makes two lines of bathtubs, model a and model b. every tub requires blending a certain amount of steel and zinc; the company has available total of 24,500 pounds of steel and 6,000 pounds of zinc. each model a bathtub requires a mixture of 120 pounds of steel and 20 pounds of zinc, and each yields a profit of $90. each model b tub produced can be sold for a profit of $70; it requires 100 pounds of steel and 30 pounds of zinc. to maintain as adequate supply of both models, the manufacturer would like the number of model a tubs made to be no more than 5 times the number of model b tubs. fine the best product mix of bathtubs.

Answer:

Assume the best product mix maximizes profits within the given constraints. If so, this a linear programming problem amenable to solution via the Simplex Method.

Here's your setup....

Let A represent the number of model A tubs and B the number of model B. The profit (to be maximized), P, will be

P = 90A + 70B

The constraints are...

1) steel: 120A + 100B

2) zinc: 20A + 30B

3) tubs: A

Now, to walk the corners of the region...

The intersection of constraint lines (1) and (2) is based on:

120A + 100B = 24,500

-6[20A + 30B = 6,000]

-80B = -11,500

B = 143.75

20A + 100 -143.75 = 24,500

20A + 14,375 = 24,500

20A = 10,125

A = 506.25

120-506.25 + 100-143.75 = 75,125 violates the steel constraint.

The intersection of constraint lines (2) and (3) is based on:

20A + 30B = 6,000

6[A - 5B = 0]

26A = 6,000

A = 3000/13

3000/13 - 5B = 0

3000/13 = 5B

600/13 = B

120-3000/13 + 100-600/13 = 360,000/13 + 60,000/13

360,000/13 + 60,000/13 = 32,308 violates the steel constraint.

The intersection of constraint lines (1) and (3) is based on:

120A + 100B = 24,500

20[A - 5B = 0]

140A = 24,500

A = 175

175 - 5B = 0

175 = 5B

35 = B

120*175 + 100*35 = 24,500 which exactly satisfies the steel constraint.

20*175 + 30*35 = 4550

175 - 5*35 = 0 which exactly satisfies the tubs constraint.

Thus, A = 175, B = 35, and

P = 90A + 70B

P = 90*175 + 70*35

P = 18,200

Assume the best product mix maximizes profits within the given constraints. If so, this a linear programming problem amenable to solution via the Simplex Method. Here's your setup.... Let A represent the number of model A tubs and B the number of model B. The profit (to be maximized), P, will be P = 90A + 70B The constraints are... 1) steel: 120A + 100B