505232 Statistics Simulation

Develop a worksheet simulation for the following problem. The management of Madeira Manufacturing Comp product. The fixed cost to begin the production of the product is $30,000. The variable cost for the product is The product will sell for $50 per unit. Demand for the product is best described by a normal probability distrib deviation of 300 units. Develop a spreadsheet simulation similar to Figure. Use 500 simulation trials to answe

a. What is the mean profit for the simulation? b. What is the probability the project will result in a loss? c. What is your recommendation concerning the introduction of the product?

Selling price per unit

$50

Variable Cost (Uniform Distribution) Smallest Value= Largest Value=

$16 $24

Demand (Normal Distribution) Mean= Standard Deviation=

1200 300

Fixed Cost=

$30,000

We will generate random numbers using Excel Worksheet function RAND Random # 0.63948 =RAND() To generate variable cost which follows a uniform distribution To generate demand which follows a normal distribution

# of units= Sales @ Less Variable costs @ Contribution= Less Fixed Costs Profit=

624 $50 = $19.22 =

$31,200 $11,993 $19,207 $30,000 -$10,793

=624 x 50 =624 x 19.22 =$31,200 - $11,993 =$19,207 - $30,000

Simulation trials Trial #

# of units=

1

1151

Sales

$57,550

Variable cost per unit 17.05

Variable cost

Contribution ( Sales Variable Costs) $19,625 $37,925

Profit = Contribution Fixed cost of $ 30,000 $7,925

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500

789 1394 965 1111 1377 1156 1012 1327 1129 1429 1331 1257 1009 1213 943 1279 1363 1339 1056 1183 1721 1099 731 1294 1547 729 1506 857 1002 840 881 1017 1127 1385 760 1616 1316 1521 979 604

$39,450 $69,700 $48,250 $55,550 $68,850 $57,800 $50,600 $66,350 $56,450 $71,450 $66,550 $62,850 $50,450 $60,650 $47,150 $63,950 $68,150 $66,950 $52,800 $59,150 $86,050 $54,950 $36,550 $64,700 $77,350 $36,450 $75,300 $42,850 $50,100 $42,000 $44,050 $50,850 $56,350 $69,250 $38,000 $80,800 $65,800 $76,050 $48,950 $30,200

16.58 20.25 19.18 16.44 18.41 16.15 22.31 17.15 20.31 19.48 19.7 17.26 19.85 22.71 19.2 22.14 16.23 22.85 18.47 23.57 18.84 23.85 21.9 22.96 18.34 16.59 18.73 16.89 17.47 21.87 23.12 17.3 17.74 22.75 16.47 21.67 22.84 20.47 21.98 21.21

$13,082 $28,229 $18,509 $18,265 $25,351 $18,669 $22,578 $22,758 $22,930 $27,837 $26,221 $21,696 $20,029 $27,547 $18,106 $28,317 $22,121 $30,596 $19,504 $27,883 $32,424 $26,211 $16,009 $29,710 $28,372 $12,094 $28,207 $14,475 $17,505 $18,371 $20,369 $17,594 $19,993 $31,509 $12,517 $35,019 $30,057 $31,135 $21,518 $12,811

$26,368 $41,471 $29,741 $37,285 $43,499 $39,131 $28,022 $43,592 $33,520 $43,613 $40,329 $41,154 $30,421 $33,103 $29,044 $35,633 $46,029 $36,354 $33,296 $31,267 $53,626 $28,739 $20,541 $34,990 $48,978 $24,356 $47,093 $28,375 $32,595 $23,629 $23,681 $33,256 $36,357 $37,741 $25,483 $45,781 $35,743 $44,915 $27,432 $17,389

-$3,632 $11,471 -$259 $7,285 $13,499 $9,131 -$1,978 $13,592 $3,520 $13,613 $10,329 $11,154 $421 $3,103 -$956 $5,633 $16,029 $6,354 $3,296 $1,267 $23,626 -$1,261 -$9,459 $4,990 $18,978 -$5,644 $17,093 -$1,625 $2,595 -$6,371 -$6,319 $3,256 $6,357 $7,741 -$4,517 $15,781 $5,743 $14,915 -$2,568 -$12,611

a. What is the mean profit for the simulation? Mean profit = Average profit of the 500 trials= Calculated using Excel Worksheet function AVERAGE

b. What is the probability the project will result in a loss?

$6,852 =AVERAGE(H45:H544)

Number of losses= Total number of trials= Therefore, probability of loss=

119 =COUNTIF(H45:H544,"