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? (1 point) Responses 20 of type A; 20 of type B 20 of type A; 20 of type B 2 of type A; 38 of type B 2 of type A; 38 of type B 30 of type A; and 10 of type B 30 of type A; and 10 of type B 38 of type A; 2 of type B

Question

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? (1 point) Responses 20 of type A; 20 of type B 20 of type A; 20 of type B 2 of type A; 38 of type B 2 of type A; 38 of type B 30 of type A; and 10 of type B 30 of type A; and 10 of type B 38 of type A; 2 of type B

Answer 1

2 of type A; 38 of type B

Let x be the number of type A tables ordered and y be the number of type B tables ordered.

The total cost is given by:

265x + 100y

The total profit is given by:

25x + 13y

Subject to the constraints:

x + y ≤ 40
25x + 13y ≥ 760
x ≥ 1
y ≥ 1

Solving the linear programming problem, we find that x = 2 and y = 38. Therefore, the store should order 2 of type A tables and 38 of type B tables to minimize cost while satisfying the constraints.