Question

Use Excel to find out the answers, show all working.

An open-top tank is to be made from a sheet of metal by bending and welding (as shown be- low). The specifications are that the volume is to be 1.0 m3 using the minimum sheet area.

Answer 1

First of all we must understand that the base dimensions of the tank are given as equal i.e "a"

The height is given as "b"

For minimum material the surface area must be minimum. It is calculated using solver add in in excel.

[To add solver add in go to office button - excel options - add ins -solver add in - go -solver add in -ok - install - ok.

You can access it from data - solver ]

1. With initial temporary values

HomeInsert Page Layout Formulas Data Review View % Cut 2 AutoSum Copy Fil- Paste в 1 u-ロ-o-스 涅涅보 Merge & Center. I s, % , 'al Conditional Format eCell Formatting as Table Styles Insert Delete Format Sort & Filter. Find & Select Format Painter 2 Clear Cells Clipboard Alignment Styles Editing A1 2 Given Volume, V= L*A*A 1m Initial arbitrary 3 values taken for 4 Length of tank, L = 1 m calculation 5 Breadth of tank, B = 1 m 6 Height of tank, H = 1 m Volume 8 Surface Area, A - 10 The condition is that the area of sheet used is minumum i.e the total surface area must be minimum 12 13 14 15 16 17 4 Sheeti Sheet2 Sheet3 9:24 PM 22/05/2019

2. Showing the formulas used in Excel

HomeInsert Page Layout Formulas Data Review View fe Σ自 @ A 臼自 in 4fcd Detine Fa mula 너 Trace Dependents, ErrowFormulas cu a Calculate Now Trace Dependents ф Error Checking Remove Arrows, QEvaluate Formula Use in Formula " watch Watch Calculation Calculate Sheet window Insert AutoSum Recently Financial Logical Text Date & Lookup & Math More Used Name Create from Selection Time Reference v &Trig-Functions. Manager Options, Function Library Defined Names Formula Auditing A1 Given Volume, V= L*B*H = 1ms 3 nitial arbitrary values taken for calculation Length of tank, Breadth of tank, B- 6 Height of tank, H = m3 Volume- C4 C5 C6 7 Surface Area, A 8 10 The condition is that the area of sheet used is minumum i.e the total surface area must be minimum 12 13 14 15 16 17 11 1 ト 커 Sheet1 Sheet2·Sheet3 9:29 PM 22/05/2019

3. Giving the parameters in solver add in and press solve

Home Insert Page Layout Formulas Data Review View Show Detail Clear Properties Hide Detail Sort Filter From From From From Other Existing Refresh Access Web Text Sources || Sort | Fitter Reapply Text to RemoveData Consolidate What-If Group Ungroup Subtotal Columns Duplicates Validation co Edit Links Connections | | All、 Analysis Get External Data Connections Sort & Filter Data Tools Outline C8 2 Given Volume, V- L*B*H 1m3 Solver Parameters Initial arbitrary values taken for 3 Set Target Cel: $C$3 Length of tank, L = 4 1 m Equal To: C/ Max By Changing Cels: ⓡyeke of: ⑨Min calculation 5 Breadth of tank, B- 1 m SC$A:$C$6 6 Height of tank, H = 1 m Subject to the Constraints: 1 m 7 Volume 5 m 8 Surface Area, A SC$7-1 Reset Al 10 The condition is that the area of sheet used is minumum i.e the total surface area must be minimum 12 13 14 15 16 Sheet2 Sheet3 14 4 ト 커 Sheet1 Sheet2· Sheet3 2/05/2019

4. Final answers obtained

Home Insert Page Layout Formulas Data Review View laめconnections坴, Show Detal " ,Solver à 7eRle pply Clear み哟匉悃邇: à Properties Hide Detail rt Filter Text to Remove Data Consolidate What-l Group Ungroup Subtotal Columns Duplicates validation. From From From From Other Existing Refresh Access Web Text Sources Advanced co Edit Links Connections | | All、 Analysis G11 Analysis Get External Data Connections Sort & Filter Data Tools Outline A1 Given Volume, V: L*A*A-1m3 2 Initial arbitrary values taken for 3 Solver Results Length of tank, L= 4 1.25998 m calculation 5 Breadth of tank, B1.25998 m Solver found a solution, All constraints and optimality conditions are satsfied Reports 6 Height of tank, H = | 0.6299 m OKeep Solver Solution 7 Volume Restore Criginal Values 8 Surface Area, A = 10 The condition is that the area of sheet used is minumum i.e the total surface area must be minimum 12 13 14 15 16 11 1 ト 커 Sheet1 Sheet2· Sheet3 22/05/2019 9:26 PM

The answer is 1.25998m, 1.25998m, 0.6299m

The area of material to be used is 4.7622 sq.m