Solve the following consumer optimization problem using Kuhn-Tucker. (Your solution should have Xi ≥ 0.) max 2x1x2 + 7 subject to 3x1 + x2 ≤ 60 and x2 ≤ 20
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Can someone solve this optimization problem using Kuhn tucker?
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- solve the question 6 with complete explanation within 10 mins or else downvoteCompany X has been unable to keep up with customer demands for product Y. They are considering two options. The first is to replace the existing tooling machine with a new machine or start a second shift to increase throughput. The cost of the new machine is $500,000. The cost of ramping up the second shift is 150,000. With the new machine option, there is a 60 percent opportunity of generating 750,000 in revenue. There is also a 40 percent opportunity of making $200 in revenue. With the second shift option, there is a 50 percent opportunity to generate $400,000 of revenue and a 50 percent opportunity to generate $100,000 of revenue. Which option would you recommend?Based on the best available econometric estimates, the market elasticity of demand for your firm’s product is −3.0. The marginal cost of producing the product is constant at $150, while average total cost at current production levels is $215. Determine your optimal per unit price if: Instructions: Enter your responses rounded to two decimal places.
- For the first week of August, the Queen Arms Hotel budgeted for 1,100 room nights at an average room rate of $140. Actual room nights for the week totaled 1,000 with an average room rate of $135. The price variance for the week was: Group of answer choices a.$5,000 unfavorable. b. $7,000 favorable. c. $5,200 favorable. d. $5,500 unfavorable.EXAMPLE 18.3 Micro Pizza Heater: Market Demand A factory renovation is needed to build a compact microwave with a new shape, which will be called the Micro Pizza Heater. The low sales-volume prediction (20,000 heaters per year) has a subjectively estimated probability of 30%. The most likely market prediction is 30,000 units sold per year. The optimistic market prediction (30,000 sold the first year, with annual increases of 5000) has a subjectively estimated probability of 10%. In all cases, the factory equipment and the market will last 5 years. The net revenue will be $10 per microwave. What is the probability distribution for the net revenue?Question 13 Given your answers above for Questions 10-12 (especially Q12), should the shop hire that third mechanic? Group of answer choices Yes, the shop should hire the third mechanic. No, the shop should NOT hire the third mechanic.
- The total cost a power plant ($/megawatts) to produce electricity is Y=12+1.3X+0.24 X2 , where X is in megawatts. The estimated selling price of electricity is (16-0.23X) per megawatts. Find the value of X that maximizes profit. Group of answer choices Less than 10 megawatts Between 10-12 megawatts Between 12-14 megawatts More than 14 megawatts DontThe total revenue of a purely competitive firm from selling 6 units of output is $48. Based on this information, the unit price of the output must be Multiple Choice $8. $42. $288. $54.Need complete solution. A company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 - 5p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a.What is the optimal number of units that should be produced and sold per month? b. What is the maximum profit per month? c.What are the breakeven sales quantities and the range of profitable demand volume?
- A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150−0.01 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $50,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved if the maximum expected demand is 6,000 units per year? What is the unit price at this point of optimal demand?A company determines that the demand function for a product can be modeled by p=220-0.02x where x is the number of units produced per week. The fixed cost is $12,000 and the variable cost is $80/unit. Find the number of units that yields the maximum profit.Is the following statement true or false: “Customers prefer product A more than product B if the customer value of product A is less than the customer value of product B." Group of answer choices False True