Conrad builds picnic tables and porch swings which he sells at flea markets. A picnic table requires six 2$\times$4's and nine 1$\times$6's. A swing uses three 2$\times$4's and six 1$\times$6's. Conrad currently has 108 2$\times$4's and 180 1$\times$6's in his inventory. If tables sell for $50 and swings sell for $30, how many of each item should Conrad make in order to maximize his revenue?
A) 15 picnic tables and 10 porch swings
B) 0 picnic tables and 30 porch swings
C) 18 picnic tables and 0 porch swings
D) 12 picnic tables and 12 porch swings

Question

Quizplus · Accepted Answer

To maximize revenue, we need to maximize the number of items produced and sold. Let's assume Conrad can sell all the items he produces.

Let's first find out how many tables and swings he can make with the inventory he has:

- With 108 2F1F1F1S1F1F1F104's, he can make 108/6 = 18 picnic tables 
- With 180 1F1F1F1S1F1F1F106's, he can make 180/9 = 20 porch swings (we have 180 left over, but since we need 6 1F1F1F1S1F1F1F106's for each swing, we can make only 180/6 = 30 swings)

Now let's calculate the profit from each item:

- A picnic table requires 6 2F1F1F1S1F1F1F104's which cost 6*104 = 624 and 9 1F1F1F1S1F1F1F106's which cost 9*106 = 954. So the total cost of making a picnic table is 624+954 = 1578. If it sells for $50, the profit is $50 - $15.78 = $34.22. 
- A porch swing requires 3 2F1F1F1S1F1F1F104's which cost 3*104 = 312 and 6 1F1F1F1S1F1F1F106's which cost 6*106 = 636. So the total cost of making a porch swing is 312+636 = 948. If it sells for $30, the profit is $30 - $9.48 = $20.52.

Since the profit from a picnic table is higher than that from a porch swing, Conrad should make more picnic tables. However, he can make only 18 tables, which will earn him 18*$34.22 = $616.76. He can also make 12 porch swings (since he has only 72 2F1F1F1S1F1F1F104's left, which is enough for only 72/3 = 24 swings), which will earn him 12*$20.52 = $246.24.

Therefore, the best choice is to make 12 picnic tables and 12 porch swings, which will earn him a total revenue of $862.

Conrad Builds Picnic Tables and Porch Swings Which He Sells ×\times×

Conrad Builds Picnic Tables and Porch Swings Which He Sells $\times$