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Allisa [31]
3 years ago
6

Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (L) and the amou

nt of capital used (C) by the following function: S = 15 L0.2 C 0.8 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 50,000 tons of steel at minimum cost. Min L + C L0.2 C 0.8 L, C (b) Solve the optimization problem you formulated in part a. Hint: When using Excel Solver, start with an initial L > 0 and C > 0. If required, round your answers to two decimal places. L = $ C = $ Cost = $
Business
1 answer:
Phantasy [73]3 years ago
6 0

Solution

S = 15 x L^{0.2} x C^{0.8}

Total cost, T = wL + rC = 50L + 100C

Total revenue, R = Output price (P) x Quantity = P x 15 x L^{0.2}x C^{0.8}

(a)

Optimization problem will be:

Max R = P x 15 x L^{0.2} x C^{0.8}

Subject to T = 50L + 100C

(b) When S = 50,000

Cost is minimized when (MPL / MPC) = w / r

MPL = \partialR / \partialL = P x 15 x 0.2 x (C / L)^{0.8} = P x 3 x (C / L)^{0.8}

MPC = \partialR / \partialC = P x 15 x 0.8 x (L / C)^{0.2} = P x 12 x (L / C)^{0.2}

MPL / MPC = (3/12) x (C / L) = 50/100

C / 4L = 1/2

4L = 2C

2L = C

Substituting in production function,

15 x L^{0.2} x C^{0.8} = S

15 xL^{0.2} x (2L)^{0.8} = 50,000

15 x 2^{0.8} x L^{0.2} x L^{0.8} = 50,000

L = 50,000 / (15 x 20.8)

L = 1,914.50

C = 2L = 3,829.00

Total cost ($) = 50 x 1,914.50 + 100 x 3,829.00 = 95,725.00 + 382,900 = 478,625.00

Note: This optimization problem can be solved without using Solver too, as shown here.

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9. You decide to run a landing page experiment to test a new carousel which highlights your top performing products. Which two r
tatiyna

Answer:

Product Performance and Ecommerce Overview

Explanation:

These are the options to the question;

Shopping Behavior Analysis

✓Product Performance

✓Ecommerce Overview

✓Sales Performance

Whenever you decide to run a landing page experiment, to test a new carousel which highlights your top performing products, the two reports that could be use to determine which

Products to highlight are Product Performance and Ecommerce Overview.

Product performance is essential to test a new carousel which highlights your top performing products so that the functionality part of the product can be known.

E-commerce overview is crucial to test a new carousel which highlights your top performing product because e-commerce gives the insight to buying and selling of the products.

5 0
2 years ago
Consider the following information for a simultaneous move game: If you charge a low price (LP) and your rival charges a LP, you
alex41 [277]

Answer:

The correct answer is the option A: For each firm charge LP.

Explanation:

To begin with, the theory called <em>''Nash Equilibrium''</em> in the field of economics, refers to a type of equilibrium in an imperfect competition market that shows the situation where two or more competitors of a same good can choose how much of that good to produce and at what price charge it in order to obtain the maximun benefit as possible in the case that all the competitors are familiar with the other competitors' strategies and results but do not know what strategy every competitor might choose.

To continue, in the case presented above, <u>the nash equilibrium for each firm is to charge low price due to the fact that if one company charges high price and the other decides to charge low price then the first company will lose a big amount of money instead of the case where both charges low price</u>.

5 0
3 years ago
An interview is an primary or secondary research
Lady bird [3.3K]

Answer:

primary

Explanation:

6 0
3 years ago
Which one of the following statements is correct if a firm has a receivables turnover of 36.5? Group of answer choices It takes
Free_Kalibri [48]

Answer:

The firm collects on its sales in an average of 10 days

Explanation:

if the receivables turnover is 36.5 it means it colect his accounts 36.5 times per year

we can convert this into a days metric:

<em>the days account is outstanding:</em>

365 days per year / we collect 36.5 per year = 10 days to collect an account on average

The acounts are collected every ten days on average.

7 0
2 years ago
At the beginning of the year, ACME had an inventory of $600,000. During the year, the company purchased goods costing $2,250,000
babunello [35]

Answer:

COGS (cost of goods sold) = $2,100,000

Gross Profit rate = 0.3

Explanation:

The formula for computing COGS (cost of goods sold) is as

COGS (cost of goods sold) = Beginning inventory + Purchases - Ending inventory

where

Beginning inventory amounts to $600,000

Purchases made during the period is $2,250,000

Ending inventory is $750,000

So, putting the values above:

COGS (cost of goods sold) = $600,000 + $2,250,000 - $750,000

COGS (cost of goods sold) = $2,850,000 - $750,000

COGS (cost of goods sold) = $2,100,000

The formula for computing Gross Profit rate is as:

Gross Profit rate = Gross Profit / Net Sales

where

Gross Profit is computed as:

Gross Profit = Net Sales - COGS

= $3,000,000 - $2,100,000

Gross Profit = $900,000

Net Sales is $3,000,000

So, putting the values above:

Gross Profit rate = $900,000 / $3,000,000

Gross Profit rate = 0.3

4 0
3 years ago
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