If the cost function of Example 4 is changed to C = 20 + 15Q + Q (a) Find the new marginal-cost function. (b) Find the new equilibrium quantities. (Use fractions.) (c) Find the new equilibrium prices. (d) Verity that the second-order sufficient condition is met.
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- Leonard Presby, Inc., has an annual demand rate of 1,000units but can produce at an average production rate of 2,000 units. Setup cost is $10; carrying cost is $1. What is the optimalnumber of units to be produced each time?The operating budget of the Western Robotics Company was $300 million last year. If the operating budget this year is 12 percent less than last year, what is this year’s operating budget? Answer $_______ million.Ocean water contains 0.9 ounce of gold per ton. Method A costs $230 per ton of water processes and will recover 85% of the metal. Method B costs $270 per ton of water processed and will recover 65% of the metal. The two methods require the same investment and are capable of producing the same amount of gold each day. If the extracted gold can be sold for $400 per ounce, which method of extraction should be used? Assume that the supply of ocean water is unlimited. Show handwritten solutions
- A firm estimates its production function as Q = -2.4 + 20*L -.5*L2 + 30*K -1.00*K2 + 15*F -.3*F2. Total cost is TC = $2*L + $2.5*K + $1.75*F. The firm can sell all the output it wishes at $200 per unit. Use Excel or otherwise to find the cost minimizing and profit-maximizing amounts of L, K and F. How much F (Fuel) should the firm use?A decision maker wishes to minimize the cost of producing a given level of total benefit. B=288. The cost function is C=6x+3y and the total benefit function is B=xy. Set up the Lagrangian and then determine levels of x and y at 5he minimum level of cost. What is the minimum value of cost?Under a marginal cost pricing option, the market price and quantity of gizmos would be: A. $64 and 15 units B. $99 and 75 units C. $43 and 230 units D. $54 and 230 units
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- Short Grass Incorporated is a distributor of golf balls. Martin's Golf Supplies is a local retail outlet which sells golf balls. Martin's purchases the golf balls from Short Grass Incorporated at $1.15 per ball; the golf balls are shipped in cartons of 72. Short Grass Incorporated pays all incoming freight, and Martin's Golf Supplies does not inspect the balls due to Short Grass' reputation for high quality. Annual demand is 159,520 golf balls at a rate of 3,691 balls per week. Martin's Golf Supplies earns 10% on its cash investments. The purchaseminus−order lead time is one week. The following cost data are available: Relevant ordering costs per purchase order $132.00 Carrying costs per carton per year: Relevant insurance, materials handling, $0.87 breakage, etc., per year What is the economic order quantity? (Round costs to the nearest cent and quantities to the nearest whole number.)Electrical Components Profit A company’s dailyprofit from the production and sale of electrical components can be described by the equation P(x) =6.45x - 2000 dollars, where x is the number of unitsproduced and sold. What level of production andsales will give a daily profit of more than $10,900?A decision maker wishes to minimize the cost of producing a given level of total benefit B = 288. The cost function is C = 6x + 3y. And the total benefit function is B = xy. Set up the Lagrangian and then determine levels of x and y at the minimum level of cost. What is the minimum value of cost?