Question

Suppose that profit for a particular product is calculated using the linear equation: Profit = 20S + 3D. Which of the following combinations of S and D would yield a maximum profit?
a. S = 0, D = 0
b. S = 405, D = 0
c. S = 0, D = 299
d. S = 182, D = 145

Answer 1

Answer:

b. S = 405, D = 0

Step-by-step explanation:

We have been given that profit for a particular product is calculated using the linear equation: $\text{Profit}=20S+3D$. We are asked to choose the combinations of S and D that would yield a maximum profit.

To solve our given problem, we will substitute given values of S and D in the profit function one by one.

a. S = 0, D = 0

$\text{Profit}=20S+3D$

$\text{Profit}=20(0)+3(0)$

$\text{Profit}=0$

b. S = 405, D = 0

$\text{Profit}=20S+3D$

$\text{Profit}=20(405)+3(0)$

$\text{Profit}=8100+0$

$\text{Profit}=8100$

c. S = 0, D = 299

$\text{Profit}=20S+3D$

$\text{Profit}=20(0)+3(299)$

$\text{Profit}=0+897$

$\text{Profit}=897$

d. S = 182, D = 145

$\text{Profit}=20S+3D$

$\text{Profit}=20(182)+3(145)$

$\text{Profit}=3640+435$

$\text{Profit}=4075$

Since the combination S = 405, D = 0 gives the maximum profit ($8100), therefore, option 'b' is the correct choice.