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- Maximize the following equation: w (x, y) = -3x² + 30x – 6y² + 48y Subject to x + y = 5 O x=2.33; y=2.67 O x=3.33; y=2.67 O x=2.33; y=3.67 O x=12.33; y=12.67Assume you are pursuing a bachelor’s degree and you have 40 hours to divide between work and school in a week. You choose the amount of time you spend on each based on the classes you take and the hours you request at work. The degree will take you 3 years to complete if you dedicate 40 hours a week and do not take summers off. Obviously, if you devote no time to school, you never get your degree. You have been going to school full time for two quarters. In the third quarter, you do not receive as much loan money as you anticipate and need. You decide to work 20 hours a week to make up the difference and take fewer classes. What is your opportunity cost? Make sure to include how this change will factor into the length of time it will take you to finish your degree.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.)
- Which one of the following is the derivative of √k? O (1/2)k-1/2 ○ (1/2)k 2k² O OoTC= 1/3 Q^3- 15Q^2 + 480Q+ 900 a) Write down the equation for MC, AFC b) Find the values of Q for which MC and AVC are minimized c) Plot the graph of MC, AFC and AVC on the same graph. CommentQ4 The output of a production process, Q, is given by the function KL Q = K+ 2L where K and L denote capital and labor. (a) Calculate the output when the capital and labor are 40 and 30 units, respectively. (b) Find the level of labor needed to produce 4 units of output when 10 units of capital are used. (c) Transpose this formula to express K in terms of Q and L. Q5 3 The equations defining a simple model of the economy are: C = 0.75Y + 18 I = 22 where C, Y and I denote consumption, national income and planned investment, respectively. Use this model to complete the following table of values and hence draw an accurate graph of C + I plotted against Y on the interval 0 < Y< 200. 100 200 C + I By drawing a second line on the diagram, calculate the equilibrium level of national income. Use your graph to explain what happens to the equilibrium level of national income when the marginal propensity to consume decreases with autonomous consumption fixed.
- Ruff makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 208 grams of protein and at least 142 grams of fat. If chicken costs 10c per ounce and grain costs 1e per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize costs? (chicken, grain) = What are the shadow costs of protein and fat? ¢ per g e per g protein fatSince MC(y) is the derivative of c(y), c(y) must be the integral of MC(y) . Select one: True Falseb.A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Inverse Method or the Cramer’s Rule, determine how many of each type of clothing should be made to use all available labor hours?
- Later, the teaching assistant in Clancy’s economics course gives him some advice. “Based on past experience,” the teaching assistant says, “working on 15 problems raises a student’s exam score by about the same amount as reading the textbook for 1 hour.” For simplicity, assume students always cover the same number of pages during each hour they spend reading. Given this information, in order to use his 4 hours of study time to get the best exam score possible, how many hours should he have spent working on problems, and how many should he have spent reading? 1 hour working on problems, 3 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours readinga.A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packagingtime. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time.The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the ??????? ?????? ?? ?????????'? ????, determine how many of each type of clothing should be made to use all available labour hours?Need all 4 parts. ...don't attempt this question f you will not solve all four parts