You manage a two-product firm. The production technology requires a mixture of capital and labor to...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
You manage a two-product firm. The production technology requires a mixture of capital and labor to produce each product. Capital is shared, while labor is specific to each of the two products. For the first product, capital (K > 0) and labor (L20) must satisfy the following, in order to produce units: 9 KL. Likewise, producing 92 units of the second product requires capital (K) and labor (now L > 0) such that: 92 KL2. In addition, total capital is limited to a maximum of 200 units. (So K 200.) Naturally, K, L, L are all required to be non-negative. Capital costs 100 per unit, labor for the first product costs 140 per unit and labor for the second product costs 175 per unit. The first product sells for 275 per unit, and the second sells for 300 per unit. 1. Initially suppose only the first product is present. Determine and interpret your optimal production plan. 2. Next suppose only the second product is present. Determine and interpret your optimal production plan. 3. Now assume both products are present. Determine and interpret your optimal production plan. 4. Repeat the three parts above assuming the first product sells for 200 per unit. 5. Fill in the following table: 91 92 MC of q with q2 fixed. MC of q2 with q fixed. 50 50 50 100 50 150 100 50 100 100 100 150 150 100 150 150 (MC is the marginal cost) 6. Write a short paragraph interpreting your findings. You manage a two-product firm. The production technology requires a mixture of capital and labor to produce each product. Capital is shared, while labor is specific to each of the two products. For the first product, capital (K > 0) and labor (L20) must satisfy the following, in order to produce units: 9 KL. Likewise, producing 92 units of the second product requires capital (K) and labor (now L > 0) such that: 92 KL2. In addition, total capital is limited to a maximum of 200 units. (So K 200.) Naturally, K, L, L are all required to be non-negative. Capital costs 100 per unit, labor for the first product costs 140 per unit and labor for the second product costs 175 per unit. The first product sells for 275 per unit, and the second sells for 300 per unit. 1. Initially suppose only the first product is present. Determine and interpret your optimal production plan. 2. Next suppose only the second product is present. Determine and interpret your optimal production plan. 3. Now assume both products are present. Determine and interpret your optimal production plan. 4. Repeat the three parts above assuming the first product sells for 200 per unit. 5. Fill in the following table: 91 92 MC of q with q2 fixed. MC of q2 with q fixed. 50 50 50 100 50 150 100 50 100 100 100 150 150 100 150 150 (MC is the marginal cost) 6. Write a short paragraph interpreting your findings.
Expert Answer:
Answer rating: 100% (QA)
To solve the optimization problems described we can use the concept of profit maximization subject to the given constraints Lets go through each part of the question 1 Optimal production plan when onl... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
Suppose that a firms production function is q = 10L1/2 K1/2 . The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a) The firm is currently producing 100 units of output and...
-
Economic Rent and Profiting from Entrepreneural Skill: Suppose, as in exercise 14.4, that you are operating a hamburger restaurant that is part of a competitive industry. Now you are also the owner,...
-
Use the correlation matrix from Problem 1 to answer the following questions. a. Compute the semipartial rSBP(SMK|AGE). b. Compute the semipartial rSMK(SBP|AGE). c. Compare these correlations to the...
-
1. What is decentralization? 2. What does control mean in a decentralized organization?
-
A piece of electronic circuitry embedded in a layer of diamond \(\left(n_{\text {diamond }}=2.42 ight.\) ) emits light. The diamond is covered by a coating of flint glass \(\left(n_{\text {flint...
-
Find the area under the standard normal curve to the right of z = 1.06.
-
Refer to the data for Auto Lavage in Exercise 99. The actual operating results for October appear below: In Exercise 99, Auto Lavage is a Canadian company that owns and operates a large automatic...
-
Which is the most component of the research report?
-
Background: In the initial contract negotiation stage, the contract price with SM was $10.1 million in cash. However, as part of the final contract negotiations, SM agreed to give EYE SPY its old...
-
Consider an Elliptic curve E1(1,6); that is the curve is defined by y2 = x + x + 6 over mod 11. a) Determine all the points in E11(1,6). Also, compute 3G corresponding to the generator point G =...
-
Is a new molecule of DNA put together using two newly made strands?
-
What types of experiments showed that living organisms are not spontaneously generated in nonliving matter? Why do you think the idea of spontaneous generation survived so longthat is, why was...
-
You are bowling with a 10-pound ball that you throw at 10 mph, and youve decided that you need to hit the pins with a ball that has more momentum. What are two possible changes you could make?
-
Nancy Burley of the University of California, Irvine, ran the following experiment: She placed red color bands on the feet of some male birds and green color bands on the feet of other male birds....
-
Why do proteins, built from instructions contained in an organisms genes, determine many of an organisms traits?
-
If Dr. Evil out that holding the earth ransom for $10,000,000 in 2017 is the same thing as demanding $1,000,000 in 1967, approximately what rate of inflation was he using to make that assumption? You...
-
Discuss the information available from the following techniques in the analysis of inorganic pigments used in antique oil paintings: (i) Powder X-ray diffraction, (ii) Infrared and Raman...
-
Toni likes to purchase round trips between the cities of Pulmonia and Castoria and other goods out of her income of $10,000. Fortunately, Pulmonian Airways provides air service and has a...
-
Figure 4.17 illustrates the case in which a consumer is better off with a quantity discount. Can you draw an indifference map for a consumer who would not be better off with the quantity discount?
-
Suppose a factory located next to a river discharges pollution that causes $2 million worth of environmental damage to the residents downstream. The factory could completely eliminate the pollution...
-
Due to the Covid recession of 2020, the U.S. government budget changed from smaller deficits to very large deficits. What impact would this have on the net exports and private sector balances, all...
-
Verify the log-likelihood in equation (16.4) for the Tobit model. In L = = In { 1-0 (x-di)} 1:y=di 122. + (y; - x) 02 (16.4) i:y;>di
-
Verify the likelihood in equation (16.5) for the two-part model. n2. (16.5) -(-)-(-2)/02 L = [] {(p;)" (1 p; )'-'} [[ ( i=1 ri=1
Study smarter with the SolutionInn App