Question

1. Your furniture store sells two types of dining room tables. The first, type A, costs $265 and you make a $25 profit on each one. The second, type B, costs $100 and you make a $13 profit on each one. You can order no more than 40 tables this month, and you need to make at least $760 profit on them. If you must order at least one of each type of table, how many of each type of table should you order if you want to minimize your cost? Possible answers :

20 of type A; 20 of type B
2 of type A; 38 of type B
30 of type A; and 10 of type B
38 of type A; 2 of type B

Answer 1

1. (5,0)

2. 20 of type A;20 of type B

3. no solution

4. -5

5.D

11 -12 7

5 12 -7

6. (-6,8)

100% right i gotchu bbs <3

Answer 2

Let x represent the number of type A table and y represent the number of type B tables.
Minimize: C = 265x + 100y
Subject to: x + y ≤ 40
25x + 13y ≥ 760
x ≥ 1, y ≥ 1

From, the graph the corner points are (20, 20), (39, 1), (30, 1)
For (20, 20): C = 265(20) + 100(20) = $7,300
For (39, 1): C = 265(39) + 100 = $10,435
For (30, 1): C = 265(30) + 100 = $8,050

Therefore, for minimum cost, 20 of type A and 20 of type B should be ordered.