Question

**Please include solver

2. A steel mill produces two types of steel alloy: boral and chromal. Production of each alloy requires three processes: Box anneal, Cold Roll, and Strand anneal.

Production capacities are:

Box anneal: 4,000 hours/month

Cold Roll: 500 hours/month

Strand anneal: 1,000 hours/month

Production rates in tons:

	Box anneal	Cold roll pass 1	Stand anneal	Cold roll pass 2
Boral	4	72	11	36
Chromal	2	Not required	20	24

The maximum demand for boral is 10,500 tons/month and for chromal 6,000 tons/month. The contributions/ton are boral: $25, and chromal: $35. What combination of boral and chromal maximizes total monthly contribution?

Answer 1

Number of Boral=X1

Number of Chromal=X2

Objective Functions= 25*X1+35*X2

Constraints:

X1=<10500

X2=<6000

4*X1+2*X2=<4000

108*X1+24*X2=<500

11*X1+20*X2=<1000

X1>=0

X2>=0

Hence, combination of boral and chromal maximizes total monthly contribution= (0,20.83)

1	B	C	D	E	F	G
2	contributions/ton for Boral	25
3	contributions/ton for Chromal	35
4
5		Boral	Chromal
6	Ton	0.00	20.83
7	contributions/ton	25	35
8		Boral	Chromal
9	Box Anneal	4	2	41.66667	=<	4000
10	Cold Roll	108	24	500	=<	500
11	Stand Anneal	11	20	416.6667	=<	1000
12		1	0	0	=<	10500
13		0	1	20.83333	=<	6000
14		1	0	0	>=	0
15		0	1	20.83333	>=	0
16	Total Contributions	729.17

Solver Parameter:

Excel Formula:

1	B	C	D	E	F	G
2	contributions/ton for Boral	25
3	contributions/ton for Chromal	35
4
5		Boral	Chromal
6	Ton	0	20.8333333333333
7	contributions/ton	25	35
8		Boral	Chromal
9	Box Anneal	4	2	=SUMPRODUCT($C$6:$D$6,C9:D9)	=<	4000
10	Cold Roll	108	24	=SUMPRODUCT($C$6:$D$6,C10:D10)	=<	500
11	Stand Anneal	11	20	=SUMPRODUCT($C$6:$D$6,C11:D11)	=<	1000
12		1	0	=SUMPRODUCT($C$6:$D$6,C12:D12)	=<	10500
13		0	1	=SUMPRODUCT($C$6:$D$6,C13:D13)	=<	6000
14		1	0	=SUMPRODUCT($C$6:$D$6,C14:D14)	>=	0
15		0	1	=SUMPRODUCT($C$6:$D$6,C15:D15)	>=	0
16	Total Contributions	=SUMPRODUCT(C6:D6,C7:D7)