Question

i. What is the impact on profit of a change in the supply of nonelectronic components? ii. What is the impact on profit if we could increase the supply of electronic components by 400 units (to a total of 5,100)? iii. In the previous question what would happen, if we could increase the supply of electronic components by 4,000 units (to a total of 8,700 units)? iv. Refer to the question about getting an additional 400 units of electronic components. What would happen if the supplier of these 400 units wanted £8 per unit rather than the current cost of £7 per unit? v. Assume that we have the opportunity to get 250 additional hours of assembly time. However, this extra time will cost us £15 per hour rather than the current cost of £10 per hour. Should we take it? vi. If we force the production of VCRs, what would be the impact on total profit? vii. How profitable must VCRs become before Anderson would consider producing them? viii. Assume that there is some uncertainty in the price for DVD players. For what range of price will the current production remain optimal? If DVD players sold for £106, what would be Anderson's new total profit?
MY QUESTION IS :

Prepare a short technical report on the above problem.

PLEASE HELP

Answer 1

Q1.

Let,

xi = number of product i to be produced where i = {VCR=1,STEREO=2,TV=3,DVD PLAYER=4}

Profit = Revenue-cost = 70x1+80x2+150x3+110x4-(3*7+2*5+1*10)x1-(4*7+2*5+1*10)x2-(4*7+4*5+3*10)x3-(3*7+3*5+2*10)x4

Objective is to maximize profit => Max 29x1+32x2+72x3+54x4

subject to,

3x1+4x2+4x3+3x4 <= 4700 (Electronic components)
2x1+2x2+4x3+3x4 <= 4500 (Nonelectronic components)
x1+x2+3x3+2x4 <= 2500 (Assembly time (hours))

xi >= 0 (non-negativity constraint)

Solving in solver we get,

Optimal solution:

VCR = 0
STEREO = 380
TV = 0
DVD Player = 1060

Maximized profit = 69400

Solver screenshot

B C D E F G H x1x2x3 x4 0 380 0 1060 Objective function 69400 5 Electronic components 3 3 4700 <= 4700 Nonelectronic 6 components 3940 <= 4500 7 Assembly time (hours) 2 2500 <= 2500 8

Solver formula

B C D E G H x1 0 X2 X3 3800 X4 1060 Objective function =29*B3+32*C3+72*D3+54*E3 5 Electronic components 3 4 4 3 -SUMPRODUCT(B5:E5,$B$3:$E$3) <= 4700 6 Nonelectronic components 2 2 4 3 =SUMPRODUCT(B6:16,$B$3:$E$3) <= 4500 7 Assembly time (hours) 1 1 3 2 =SUMPRODUCT(B7:E7,$B$3:$E$3) <= 2500

Sensitivity report

8 Final Reduced Objective Value Cost Coefficient 0 -1 3800 Allowable Allowable Increase Decrease 1 1E+30 40 1.666666667 8 1E+30 105 12 1060 0 6 Variable Cells 7 Cell Name 9 $B$3 x1 10 $C$3 x2 11 $D$3 x3 $E$3 x4 13 14 Constraints 15 16 Name $F$5 Electronic components 18 $F$6 Nonelectronic components $F$7 Assembly time (hours) 17 Final Shadow Constraint Allowable Value Price R.H. Side Increase 4700 2 4700 2800 3940 0 4500 1 E+30 2500 24 2500 466.6666667 Allowable Decrease 950 560 1325 19 20

i)

There is no impact on increase on Non electronic components as there is slack. Also, decrease upto another 560 units (Slack quantity) will also have no impact on profit. However decrease of more than 560 units will surely have an impact on profit

ii)

Electronic components have a shadow price of 2 and this shadow price is valid till increase of 2800 units which means for every additional unit of Electronic components will increase profit by $2 hence 400 units of additional Electronic components will increase profit by 400*2 = 800. New profit would be 69400+800 = 70200

iii)

As allowable increase for Electronic components is 2800 units so increase of 4000 units will surely change profit by we can not determine that by looking at the solver report as present shadow price will not remain valid beyond allowable increase. Hence we need to re-run the solver to find the change in profit

iv)

Yes. additional units of electronic components would be a buy from the supplier as increase of cost 400 is less than generated profit for another 400 units which is 800

v)

Assembly time has shadow price of 24 per hour which is valid till increase of 466.6666667 hours which means every additional hour of assembly time will increase profit by 24. As profit generated is more than the cost we should take it

vi)

Profit will decrease with every additional unit of forced production of VCRs

vii)

As reduced cost of VCR is -1 profit on VCR needs to be at least 30 before Anderson would consider producing them

viii)

Current production plan will remain optimal for following range of price of DVD players:

Lower range = (110-5) = 105 and upper range = (110+10) = 120

If DVD players are sold for 106 ,new total profit will be 69400-4*1060 = 65160