A manager in charge of new product development can hire engineers and market researchers.The annual salary of an engineer is $40,000,while a market researcher receives $20,000.The marginal contributions of engineers and market researchers are: Based on the above information,how should the manager with an annual budget of $160,000,allocate this budget in order to maximize the number of new products developed?
A)Hire 2 engineers and 1 market researcher.
B)Hire 3 engineers and 2 market researchers.
C)Hire 4 engineers and 3 market researchers.
D)Hire 4 engineers and 1 market researcher.

Question

A manager in charge of new product development can hire engineers and market researchers.The annual salary of an engineer is $40,000,while a market researcher receives $20,000.The marginal contributions of engineers and market researchers are:  Based on the above information,how should the manager with an annual budget of $160,000,allocate this budget in order to maximize the number of new products developed?
A)Hire 2 engineers and 1 market researcher. 
B)Hire 3 engineers and 2 market researchers. 
C)Hire 4 engineers and 3 market researchers. 
D)Hire 4 engineers and 1 market researcher.

Quizplus · Accepted Answer

Let's assume that hiring "x" number of engineers and "y" number of market researchers will result in the development of "N" number of new products. We want to maximize N, given the budget constraint.

The total cost of hiring "x" engineers and "y" market researchers will be:

Total Cost = 40,000x + 20,000y

We know that the budget constraint is:

40,000x + 20,000y ≤ 160,000

Simplifying this inequality, we get:

2x + y ≤ 8

Now, let's look at the marginal contributions of the two types of employees:

Marginal Contribution of an Engineer = N / x 
Marginal Contribution of a Market Researcher = N / y

Substituting the values given in the problem statement, we get:

11 / x = 3 / y

Simplifying, we get:

y = (3x) / 11

Now we can rewrite the budget constraint only in terms of one variable:

40,000x + 20,000[(3x) / 11] ≤ 160,000

Simplifying this inequality, we get:

x ≤ 3.67

Since we can't hire a decimal number of employees, we can only hire 3 engineers, which gives us:

y = (3 * 3) / 11 = 0.82

Again, we can't hire a fraction of an employee, so we can only hire 2 market researchers.

Therefore, the optimal choice is to hire 3 engineers and 2 market researchers, which is option B.

A Manager in Charge of New Product Development Can Hire