Question

A coffee shop orders at most $3,500 worth of coffee and tea. The shop needs to make a profit of at least $1,900 on the order. The possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea:
6c + 13t ≤ 3,500
3.50c + 4t ≥ 1,900

Which graph's shaded region represents the possible combinations of coffee and tea for this order?

Answer 1

Answer:

Which graph's shaded region represents the possible combinations of coffee and tea for this order?

Answer 2

Answer:

Possible orders are

1) 542.86 pounds of coffee

2) 583.33 pounds of coffee

3) 497.64  pounds of coffee  and 39.53 pounds of tea

Step-by-step explanation:

Given :    A coffee shop orders at most $3,500 worth of coffee and tea. The shop needs to make a profit of at least $1,900 on the order.

Which graph's shaded region represents the possible combinations of coffee and tea for this order.

Let   c = pounds of coffee and t = pounds of tea

Inequality becomes,

6c + 13t ≤ 3,500

3.50c + 4t ≥  1,900

We plot these equation on graph

Taking c on x - axis and t on y - axis.

Consider 1) 6c + 13t ≤ 3,500

Let, 6c + 13t = 3500

When c = 0

13t = 3500

⇒ t = 296.23

When t = 0

6c = 3500

⇒ c = 583.33

Thus, point (0, 296.23) and (583.33, 0)

Similarly for  2) 3.50c + 4t ≥  1,900

When c = 0

4t = 1900

⇒ t = 475

When t = 0

3.50c = 1900

⇒ c = 542.86

Thus, point (0, 475) and (542.86, 0)

Plot these point to obtain the graph as shown below.

Thus, the region Common in both graph has coordinate  (542.86, 0) , (583.33, 0) and (497.64, 39.53)

Thus, graph's shaded region common in both graph represents the possible combinations of coffee and tea for this order is made by the points  (542.86, 0) , (583.33, 0) and (497.64, 39.53)

Possible orders are

1) 542.86 pounds of coffee

2) 583.33 pounds of coffee

3) 497.64  pounds of coffee  and 39.53 pounds of tea