Applied Problems # 2 Dimex Fabrication Co., a small manufacturer of sheet-metal

Question

Applied Problems # 2

Dimex Fabrication Co., a small manufacturer of sheet-metal body body parts for a major US automaker, estimates its long-run production to be
Q= -0.015625K(three)L(three) + 10 K (two) L (two)

NOTE: the numbers in number in ( ) meaning as exponents

where Q is the number of body parts producted daily, K is the number of sheet-, metal presses in its manufacturing plant, and L is the number of labor-hours per day of sheet-metal workers employed by Dimex. Dimex is currently operating with eight sheet-metal presses.

We have to answer questions a, b, and c.

a. What is the total product function for Dimex? The average product function? The marginal product function?

b. Managers at Dimex can expect the marginal product of additional workers to fall beyond what level of labor employment?

c. Dimex plan to employ 50 workers. Calculate total product, average product, and marginal product.

Please email to taxdoc10@gmail.com

Explanation / Answer

a. Total product function is MPL/MPK where MPL and MPK are the first derivatives with respect to L and K MPL=-0.015625K^3L^3 + 10 K^2 L^2 =-0.046875K^3L^2+20K^2L MPK -0.046875K^2L^3+20KL^2 Now we solve MPL/MPK (-0.046875K^3L^2+20K^2L)/(-0.046875K^2L^3+20KL^2)=-K/L Average prduct is our function divided by Q (-0.015625K^3L^3 + 10 K^2 L^2)/Q Marginal product is the derivative of average product with respect to Q (-0.015625K^3L^3)/Q + (10 K^2 L^2)/Q =0.015625K^3L^3 -10 K^2 L^2 It is similar to our original function except the signs changed B. They can expect it to fall when MPL=0 is maximized -0.015625K^3L^3 + 10 K^2 L^2 =-0.046875K^3L^2+20K^2L we solve for L and see L=1280/3K C. We plug 50 into our functions we found in the first problem and multiply by Price For total cost P*-K/L=-KP/50 Average Product -1953.125K^3 + 25000 K^2/Q For Marginal product 1953.125K^3 - 25000 K^2/Q Hope this helps

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.