Let's assume you want to order x number of type A tables and y number of type B tables. Since you need to order at least one of each type, x and y should be greater than or equal to 1.
The cost of type A table is $265, and you make a $25 profit on each one. So, the net cost for each type A table is $265 - $25 = $240. The total cost for x type A tables would be 240x.
Similarly, the cost of type B table is $100, and you make a $13 profit on each one. So, the net cost for each type B table is $100 - $13 = $87. The total cost for y type B tables would be 87y.
You want to minimize the cost, so you need to minimize the total cost, which is 240x + 87y.
Subject to the constraints:
- x, y >= 1 (since you need to order at least one of each type)
- x + y <= 40 (you can order no more than 40 tables)
To find the minimum cost, you can use linear programming techniques or graph the feasible region and calculate the cost at each corner. However, given the small number of variables and constraints in this particular problem, we can solve it by manually checking all possible combinations of x and y.
Considering the constraints, the possible values for x and y are:
(x, y) = (1, 39), (2, 38), ..., (39, 1)
Calculating the total cost for each combination:
- For (1, 39): 240(1) + 87(39) = $3,633
- For (2, 38): 240(2) + 87(38) = $3,466
- ...
- For (39, 1): 240(39) + 87(1) = $9,513
The minimum cost is $3,466, which corresponds to ordering 2 type A tables and 38 type B tables.
Your furniture store sells two types of dining room tables. The first type A, costs $265 and you make a $25 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 one of each of table how many of each type of table should you order at least one of each type of table how many of each type should you order if you want to minimize your cost
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