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
20 of type A; 20 of type B
2 of type A; 38 of type B
30 of type A; 10 of type B
38 of type A; 2 of type B
To minimize the cost, you should order 2 of type A and 38 of type B.
Here's the explanation:
The total cost of ordering 2 of type A tables would be 2 * (265 + 25) = $580.
The total cost of ordering 38 of type B tables would be 38 * (100 + 13) = $4,674.
So the total cost of ordering 2 of type A and 38 of type B tables would be $580 + $4,674 = $5,254.
If you order 20 of type A and 20 of type B, the total cost would be 20 * (265 + 25) + 20 * (100 + 13) = $8,700.
If you order 30 of type A and 10 of type B, the total cost would be 30 * (265 + 25) + 10 * (100 + 13) = $9,150.
If you order 38 of type A and 2 of type B, the total cost would be 38 * (265 + 25) + 2 * (100 + 13) = $9,648.
Therefore, ordering 2 of type A and 38 of type B would result in the lowest cost.
To determine the best combination of tables to order in order to minimize cost, we need to consider the cost and profit associated with each type of table.
Let's calculate the cost and profit for each combination:
1. 20 of type A; 20 of type B:
Total cost = (20 * $265) + (20 * $100) = $5,300 + $2,000 = $7,300
Total profit = (20 * $25) + (20 * $13) = $500 + $260 = $760
2. 2 of type A; 38 of type B:
Total cost = (2 * $265) + (38 * $100) = $530 + $3,800 = $4,330
Total profit = (2 * $25) + (38 * $13) = $50 + $494 = $544
3. 30 of type A; 10 of type B:
Total cost = (30 * $265) + (10 * $100) = $7,950 + $1,000 = $8,950
Total profit = (30 * $25) + (10 * $13) = $750 + $130 = $880
4. 38 of type A; 2 of type B:
Total cost = (38 * $265) + (2 * $100) = $10,070 + $200 = $10,270
Total profit = (38 * $25) + (2 * $13) = $950 + $26 = $976
From the combinations above, the combination that minimizes cost is 2 of type A and 38 of type B, resulting in a total cost of $4,330.
To minimize your cost, you need to maximize your profit while also considering the constraints given.
Let's calculate the profit for each option:
Option 1: 20 of type A; 20 of type B
Profit from the type A tables: 20 * ($265 - $25) = $4,800
Profit from the type B tables: 20 * ($100 - $13) = $1,740
Total profit: $4,800 + $1,740 = $6,540
Option 2: 2 of type A; 38 of type B
Profit from the type A tables: 2 * ($265 - $25) = $480
Profit from the type B tables: 38 * ($100 - $13) = $2,772
Total profit: $480 + $2,772 = $3,252
Option 3: 30 of type A; 10 of type B
Profit from the type A tables: 30 * ($265 - $25) = $7,200
Profit from the type B tables: 10 * ($100 - $13) = $870
Total profit: $7,200 + $870 = $8,070
Option 4: 38 of type A; 2 of type B
Profit from the type A tables: 38 * ($265 - $25) = $8,840
Profit from the type B tables: 2 * ($100 - $13) = $174
Total profit: $8,840 + $174 = $9,014
Therefore, to minimize your cost, you should order 38 of type A and 2 of type B.