3. Find the maximum value of Q = 10√KL subject to the cost constraint K+4L = 16. Estimate the change in the optimal value of Q if the cost constraint is changed to K+4L =17. Interpret the meaning of Lagrange multiplier.
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- What is the average variable cost of washing 90 cars? is the answer 4 or .7?The total cost (in hundreds of dollars) of producing x calculators per day is given by the equation. 20- 15- 10- C(x) = 6 + /2x + 32 Osx< 50 Perform the following calculations and interpret the results. 10 20 30 40 50 Production C'(x) =U %D Cost (hundred dollars)A small business sells T-shirts during the Lasallian Week Festival. It is estimated that the variable cost to produce one T-shirt is 175 pesos. Also, the total cost to produce 60 T-Shirts is 15000 pesos. T-shirts are sold at a price of 456.25 pesos each. a. Find the total cost model. C(x)= b. How many T-shirts must be sold to break even? T-shirts c. How many T-shirts must be sold to make profit of 9000 pesos? 32 T-shirt (note: do not use space and comma for your answer)
- Hi, I have been trying to compute the optimal values from this lagrangian. But I can't seem to find a way to get the values from the answer key. I attached both the question and answers. Could you please explain to me how to get these values from the first-order conditions? Thank you very muchThe total profit P(x) (in thousands of dollars) from the sale of x hundred thousand pillows is approximated by P(x) = -x° + 12x + 144x – 400, x25. Find the number of hundred thousands of pillows that must be sold to maximize profit. Find the maximum profit. The maximum profit is $ The maximum profit will occur when pillows are sold.3. Minimize the following total cost function: TC = Q³ – 10Q2 + 48Q + 46.
- The cost, in thousands of dollars, of airing x television commercials during a sports event is given by C(x) = 20 + 3,000x + 0.09x² (a) Find the marginal cost function C'(x). HINT (See Example 1.] C'(x) = Use it to estimate how fast the cost is Increasing when x- 4. thousand dollars per television commercial Compare this with the exact cost of alring the fifth commercial. The cost is going up at the rate of $ per television commercial. The exact cost of airing the fifth commercial is $ Thus, there is a difference of $ (b) Find the average cost function C, and evaluate C(4). HINT [See Example 2.] C(x) = C(4) - thousand dollars per television commercial What does the answer tell you? The average cost of airing the first four commercials is $ per commercial.MC=500Q2√Q3+5 (b) Find the total cost functionThe total cost (in dollars) of producing x food processors is C(x) = 1600 + 40x – 0.7x2. (A) Find the exact cost of producing the 21st food processor. (B) Use the marginal cost to approximate the cost of producing the 21st food processor. ..... (A) The exact cost of producing the 21st food processor is $ 11.3. (B) Using the marginal cost, the approximate cost of producing the 21st food processor is $
- Technology B uses 4 workers and 2 tonnes of coal to produce 100 meters of cloth. The worker's wages cost $10 and coal costs $5. We have previously calculated that the total cost of production is $50 and that the vertical intercept of the isocost line is 10.If there was a technology that used 1 more worker, how much would it have to decrease the coal required in order to cost the same? (Note: this is the absolute value of the slope of the isocost line.)A cost function is given. C(q) = 3600 + 5q-0.02q² + 0.00039³ (a) Find the average cost and marginal cost functions. +5 -0.02q +0.0003q average cost 3600 9 marginal cost 5 -0.04q+0.0009q (b) Use graphs of the functions in part (a) to estimate the production level that minimizes the average cost. (Round your answer to the nearest integer.) 194 ✓ units (c) Use calculus to find the minimum average cost. (Round your answer to two decimal places.) $ 32.41 X (d) Find the minimum value of the marginal cost. (Round your answer to two decimal places.) $ 4.56Assume that it costs a company approximately C(x) = 400,000 + 140x + 0.003x? dollars to manufacture x smartphones in an hour. (a) Find the marginal cost function. 400,000 – 0.000009 Use it to estimate how fast the cost is increasing when x = 10,000. 2$ per smartphone Compare this with the exact cost of producing the 10,001st smartphone. The cost is increasing at a rate of $ per smartphone. The exact cost of producing the 10,001st smartphone is $ Thus, there is a difference of $ (b) Find the average cost function C and the average cost to produce the first 10,000 smartphones. C(x) = C(10,000) = $ (c) Using your answers to parts (a) and (b), determine whether the average cost is rising or falling at a production level of 10,000 smartphones. -Select--- at a production level of 10,000 smartphones. The marginal cost from (a) is --Select--- than the average cost from (b). This means that the average cost is
