Question

To manufacture an automobile requires painting, drying, and polishing. Epsilon Motor Compary produces three types of cars, the Deita, the Beta, and the Sigma. EachDelta requires 9 hours for painting, 2 hours for drying, and 5 hours for polishing. A Beta requires 33 hours for painting, & hours for drying, and 6 hours for polishing, anda Sigma requires 4 hours for painting, 3 hours for drying, and 2 hours for polishing. If the company has 190 hours for painting, 66 hours for drying, and 54 hours forpolishing per month, how many of each type of car are produced?GThe Epsilon Motor Company produces:__ Deltas__ Betas__ Sigmas in a month

Answer 1

Let d represent the number of Deltas produced

Let b represent the number of Betas produced

Let s represent the number of Sigmas produced

Each Delta requires 9 hours of painting. Each Beta requires 33 hours of painting and each Sigma requires 4 hours of painting. If the company has 190 hours of painting, then the equation representing this situation is

9d + 33b + 4s = 190

Each Delta requires 2 hours of drying. Each Beta requires 8 hours of drying and each Sigma requires 3 hours of drying. If the company has 66 hours of drying, then the equation representing this situation is

2d + 8b + 3s = 66

Each Delta requires 5 hours of polishing. Each Beta requires 6 hours of polishing and each Sigma requires 2 hours of polishing. If the company has 54 hours of polishing, then the equation representing this situation is

5d + 6b + 2s = 54

From the third equation, if we divide both sides by 2, we have

2.5d + 3b + s = 27

s = 27 - 2.5d - 3b

We would substitute s = 27 - 2.5d - 3b into the first and second equations. By substituting s = 27 - 2.5d - 3b into the first equation, we have

9d + 33b + 4(27 - 2.5d - 3b) = 190

9d + 33b + 108 - 10d - 12b = 190

33b - 12b + 9d - 10d = 190 - 108

21b - d = 82 equation 4

By substituting s = 27 - 2.5d - 3b into the second equation, we have

2d + 8b + 3(27 - 2.5d - 3b) = 66

2d + 8b + 81 - 7.5d - 9b = 66

2d - 7.5d + 8b - 9b = 66 - 81

- 5.5d - b = - 15

b = - 5.5d + 15

We would substitute b = - 5.5d + 15 into equation 4. We have

21(- 5.5d + 15) - d = 82

- 115.5d + 315 - d = 82

- 115.5d - d = 82 - 315

- 116.5d = - 233

d = - 233/- 116.5

d = 2

We would substitute d = 2 into b = - 5.5d + 15. We have

b = - 5.5 * 2 + 15 = - 11 + 15

b = 4

We would substitute b = 4 and d = 2 into s = 27 - 2.5d - 3b. We have

s = 27 - 2.5 * 2 - 3 * 4 = 27 - 5 - 12

s = 10

Therefore, the Epsilon motors produce 2 Deltas, 4 Betas and 10 Sigmas in a month