write the Minimum amount of bookcases that can be built: x , Minimum amount of TV stands that can be built: y Answer

Question

In Andrew’s Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same time to assemble. He figures he has time to make at most 1818 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00$20.00 and the materials for each TV stand cost him $40.00$40.00. He has $600.00$600.00 to spend on materials. Andrew makes a profit of $60.00$60.00 on each bookcase and a profit of $100.00$100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit.

Using the information in the problem, write the constraints. Let x represent number of bookcases, and y represent number of TV stands.

Answer 1

As stated, let x be the number of bookcases and y be the number of TV stands.

"he has time to make at most 18 pieces of furniture": means that x + y < 18

"he has $600.00 to spend on materials" means 20x + 40y < 600 (since bookcases (x) have $20 of material each and TV stands (y) have $40 of material each. But we can simplify this equation by dividing both sides by 20 to get: x + 2y < 30.

Since his profit is $60 per bookcase (x) and $100 per TV stand (y) then his total profit is:

P = 60x + 100y

Graph each inequality:

Find each of the corner points A, B, C, and D (for instance A = (0, 0) meaning zero bookcases are made and zero TV stands are made. Calculate the profit. For (0, 0) there is zero profit. Do the same calculation for points B, C, and D and whichever is biggest is the correct answer.