Question

The Martinez Model Car Company produces four different radio-controlled model cars based on exotic production models: Ferrari, BMW, Lotus, and Tesla. Each model requires production in five departments: molding, sanding, polishing, painting, and finishing.

The number of minutes required for each product in each department, the selling price per unit, and the minutes available in each department each day are shown below.

	Ferrari	BMW	Lotus	Tesla	Minutes Available
Molding	5.00	3.50	1.00	3.00	600
Sanding	4.00	3.20	2.00	3.65	600
Polishing	3.50	2.00	3.00	1.00	480
Painting	3.75	3.25	1.75	2.00	480
Finishing	4.00	1.00	2.00	3.00	480
Price	$350.00	$330.00	$270.00	$255.00

1) What is the optimal maximum profit? (Round your answer to 2 decimals.)

2) For the optimal solution, how many Tesla automobiles should be produced? (Round your answer to the nearest whole number.)

a. 0

b. 56

c. 103

d. 59

3)The optimal solution that maximizes total profit is:  

(Round your answer to the nearest dollar.)

a. 21700

b. 21750

c. 21800

d. 21850

Answer 1

x, - no. of ferrari bord alltomobiles non no. of BMW automobiles - my a ho. of Lotes automobiles. kyy no. of Tesla automobiles , [ a 86 manimize 3500, + 33042 +29003+25514 Constraints 50 + 3.502t Miz t sny 2.600 421 + 3.202 + 2N;+ 3.6574 2 600 3.500+ 24 +393 of my ¿ 480 3.759, +3.257% +17503 +2 My [480 un, tha +243 + 3ny 2480 restrictions equations 50,4 3.592 & nat any ta5 = 600 un + 3.202 + 213 + 3.65 ny. +46 = 600 3.59, +232 + 3mg + my +27 = 480 3.757, +3.2512 +1.7573 +234 + Mg =480 44, + ng + 2^3 +34 + mq=480.

we will use simplex method of linear programming to solve the above equations

X, 1 X5 1 712 120 16/5 150 х7 1/2 X4 з 73/20o 1 2 3 -255 X6 o 1 o o o o x1 o o 1 o o o xs o o o 1 o o X, o o o o 1 o o o o o 960/7 600 600 480 480 480 o 128 13/4 1 -330 1/4 2 -270 120

X3 1 X, 1 X, o 1/2 120 16/5 1 150 1/2 2 X4 з 73/200 1 2 3 -255 X, o o 1 o o o з 114 2 -270 X8 o o o 1 o o 960/7 X, o o o o 1 o o o o o 15/4 ь 600 600 480 480 480 o o o o o 13/4 128 4 120 -350 -330

1/5 3/5 600 6/5 5/4 100 X, 1 о о o o 0 X2 1/10 2/5 -9/20 5/8 -9/5 -85 23/10 х1 ҳ6 X7 Хs Xə 1 -11/10 Х; 1/5 -4/5 -1/10 -3/4 -4/5 70 x6 o 1 о o o o X7 o o 1 o o o Хs o o o 1 o o X, o o o o 1 o ь 120 120 60 30 о 42000 600/23 -1/4 30 6/5 3/5 о -200 -45

X, о 1 120 120 х1 X6 1 о 11/5 о 600/11 X7 о X4 1/2 13/20 -914 -3/4 1/2 55 X5 1/3 o 5/6 -1/12 2/3 -190/3 X6 o 1 о o o o x7 o o 1 o o o Хs o o o 1 o o X, -16 -1 -23/12 -5/6 516 500/3 120 60 30 о о 1 o 20 240/17 Хя Хя Z о о 0 17/8 -3/2 -385 42000

Х. X9 29/34 23/102 1800/17 3600/29 X5 19/51 22/255 97 / 102 97/68 -1/51 1512/17 X, X, X; x 1 оо X6 o o o X7 o o o х, о 1 о x o o 1 z o o o 6048/97 -81/68 X6 o 1 o o o o X7 o 0 1 o o o Хs -8/17 -88 / 85 -24/17 8/17 12/17 3080/17 -151/204 300/17 -6/17 -2/51 -20/51 240/17 -1/34 25/102 360/17 -37/51 -4000/51 -1375/17 800/51 806400/17

X5 X9 X, -58/97 X7 о о Хs 12/485 467/1455 179/582 5112/97 76680/467 88/1455 68/97, -352/ 485 -28/291 6048/97 11340/11 X, X, X, X4 x 1 o o o х4 o o o 1 X7 o o o o Х, o 1 оо Х; o o 1 о 7 o o o o 2977/2910 -1104/ 485 -995/1164 8916/97 267480/2977 81/97 24/97 2/97 -124/291 -26/1455 -351/ 485 -21400/291 3504/97 о o 104 / 485 332/ 485 47/194 2232/97 5500/97 0 11880 /97 2300/291 5090400/97

X7 ха X9 X6 -2560/2977 1940/2977 -934/2977 2568/297 1714/2977 71040/2977 35520/857 -176/2977 -1760/2977 -136/2977 169440/2977 X, x 1 х4 o Хs o х, о Х; o z o X, X3 X4 X5 o o o o o o 1 о o o o 1 1 o o o o 1 o o o o o o 2430/2977 2910/2977 -6624/2977 -4975/5954 267480/2977 60/229 4/229 40/229 -101/229 8640/229 140/229 162/229 -212/229 -83/229 20160/229 347500/2977 214000/297 -122520/2977 -159400/297 175898400/297

X7 X9 X, -1280 / 857 -467/857 1284/857 35520/857 2977/1714 68/857 500/857 -72/857 -448/857 50400/857 4975/3428 X, o o o 1 o o X, o o o o 1 o X4 o 1 o o o o X5 o о 1 o o o -370/857 895/1714 -834/857 106680/857 X, 1313/1714 -340/857 -191/857 716/857 48000/857 Х3 1079/1714 60/857 437/857 -328/857 о 88320/857 z 79700/857 31500/857 36600/857 33480/857 о 52538400/857

So the optimal solletion is. 220, nu= 50400 n. 72 88320 O 857. 48000 857 857 M, 50, ma = 556 , ngi = 103 , My = 59 Ferran automobiles to be produced=0 Bmio automobiles to be produced = 56 Lotus automobiles to be produced =103 Tesla automobiles to be produced 25.9 manimum profit. = 52538400 857 = $ 61,305