Solver Function

[jack0508]

I can't figure out how to solve this problem:

I am working with a larger data set but here is a quick example:

Investment Type A:
return cost
option1: 5% $3000
option2: 6% $4500
option3: 7% $7000

Investment Type B:
return cost
option1: 4% $6500
option2: 6% $3000
option3: 9% $6200

I can invest $14,000 or less. I must invest in two options from Type A and one option from Type B. How do i calculate the optimal mix?

 

[shg]

Solver can't solve that problem, because the two least expensive investments in each category total > $14K. But this is the idea:

<TABLE style="WIDTH: 456pt; BORDER-COLLAPSE: collapse" border=0 cellSpacing=0 cellPadding=0 width=607><COLGROUP><COL style="WIDTH: 37pt" span=2 width=49><COL style="WIDTH: 40pt; mso-width-source: userset; mso-width-alt: 2450" width=54><COL style="WIDTH: 37pt" width=49><COL style="WIDTH: 305pt; mso-width-source: userset; mso-width-alt: 18578" width=406><TBODY><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #f3f3f3; WIDTH: 37pt; HEIGHT: 12pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl31 height=16 width=49>Option</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #f3f3f3; WIDTH: 37pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl31 width=49>Return</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #f3f3f3; WIDTH: 40pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl31 width=54>Cost</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #f3f3f3; WIDTH: 37pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl31 width=49>Choose</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #f3f3f3; WIDTH: 305pt; BORDER-TOP: windowtext 0.5pt solid; BORDER-RIGHT: windowtext 0.5pt solid" class=xl31 width=406> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>A1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>5%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 3,000 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>A2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>6%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 4,500 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>A3</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>7%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 7,000 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>0</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #e7e7e7; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl34 align=right>2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37>D5: =SUM(D2:D4)</TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>B1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>4%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 6,500 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>0</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>B2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>6%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 3,000 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16>B3</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl33 align=right>9%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 6,200 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 align=right>1</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: #e7e7e7; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl34 align=right>2</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37>D9: =SUM(D6:D8)</TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: white; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32 height=16> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37> </TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #f3f3f3; WIDTH: 37pt; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl35 height=16 width=49>Total</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl38> 16,700 </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37>C11: =SUMPRODUCT(C2:C8,D2:D8)</TD></TR><TR style="HEIGHT: 12pt" height=16><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext 0.5pt solid; BACKGROUND-COLOR: #f3f3f3; WIDTH: 37pt; HEIGHT: 12pt; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl35 height=16 width=49>ROI</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl36 align=right>6.93%</TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl39> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl32> </TD><TD style="BORDER-BOTTOM: windowtext 0.5pt solid; BORDER-LEFT: windowtext; BACKGROUND-COLOR: white; BORDER-TOP: windowtext; BORDER-RIGHT: windowtext 0.5pt solid" class=xl37>B12: =SUMPRODUCT(B2:B8,C2:C8,D2:D8)/SUMPRODUCT(C2:C8,D2:D8)</TD></TR></TBODY></TABLE>


Maximize B12 by changing the six Choose cells with constraints that

o the Choose values are binary
o the totals of each category is 2
o the total amount is <= the amount available

That maximizes the ROI versus maximizing the dollars returned.

 

[jack0508]

Thanks! That was exactly what I needed.

 

[shg]

You're welcome, glad it helped.