The next 4 questions refer to the following: A manager in charge of new product

Question

The next 4 questions refer to the following:
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 contribution of engineers and market researchers are:

Engineers (E)                                       Market Researchers (R)
                          Additional                                                 Additional
Worker              New Products               Worker                 New Products
1st                         2400 1st 800
2nd                        2000 2nd 700
3rd 1600 3rd 600
4th                        100 4th 500
5th 400 5th 400


1. State the rule for determining the optimal number of engineers and market researchers




2. Given an annual budget of $140,000, how many engineers and market researchers should be hired?



3. How many new products will be developed when the product development budget is allocated optimally?

4) If the manager spends $140,000 to hire 2 engineers and 3 market researchers, will such a decision yield a cost eficient combination? Why or why not?

Explanation / Answer

(1) Optimization rule:

(Marginal contribution / Salary)Engineers = (Marginal contribution / Salary)Market researchers

(2)

This rule is satisfied only when number of engineers = 3 & number of market researchers = 1. In each case, the ratio is 0.04.

So,

Total cost = 3 x ($40,000) + 1 x ($20,000) = $120,000 + $20,000 = $140,000

(3)

Number of new products developed = 1600 + 800 = 2,400

(4)

Cost for this hiring combination will be = 2 x $40,000 + 3 x $20,000 = $80,000 + $60,000 = $140,000

But, (Contribution / Salary) ratio will be (2,000 / 40,000) = 0.05 for engineers, and (600 / 20,000) = 0.03 for market researchers. So this will be an inefficient combination even though total cost will be the same as before.

ENGINEERS (Salary $40,000) MARKET RESEARCHERS (Salary $20,000) Number Marginal Contribution ($) Contribution/Salary Number Marginal Contribution ($) Contribution/Salary 1 2400 0.06 1 800 0.04 2 2000 0.05 2 700 0.035 3 1600 0.04 3 600 0.03 4 100 0.0025 4 500 0.025 5 400 0.01 5 400 0.02

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