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equilibrium can be expressed as:
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Chapter 16 Solutions
Numerical Methods for Engineers
- A green grocer’s daily profit from the sale of two brands of orange juice is given by P(x , y) = (x – 30)(70 – 5x + 4y) + (y – 40)(80 + 6x – 7y) where x is the price per gallon bottle in dollars of the first brand and y is the price per gallon bottle in dollars of the second brand. The profit is also measured in dollars. Currently, the first brand sells for 50 dollars per gallon bottle and the second brand for 52 dollars per gallon bottle. (a) Use marginal analysis to estimate the change in the daily profit that will result if the grocer raises the price of the first brand by fifty cents per gallon bottle but decreases the price of the second brand by seventy-five cents per gallon bottle and find the stationary points of the profit function P(x , y).arrow_forwardThank youarrow_forwardFind f-l (n) for 8cn) = n2-6n and its %3D domarn.arrow_forward
- The cost C of producing t units is given by C(t) = 3t² + 9t, and the revenue R generated from selling t units is given by R(t) = 41² +t. For what values of t will there be a profit? OA. There will be a profit when more than 8 units are sold. OB. There will be a profit when more than 9 units are sold OC. There will be a profit when more than 10 units are sold. OD. There will be a profit when 0 units are sold.arrow_forwardFind and simplify f(a + h) − f(a) h for the following reaction F(x)=8x square -14x+7arrow_forwardA ball is shot into the air from a bridge, and its height, y, in feet, above the ground t seconds after it is thrown is given by y=f(t)=−16t2+54t+38arrow_forward
- y = x² + 1 y = 2r – 2 -1arrow_forwardA boat has a diesel fuel tank capacity of 100 L. A particular gas station near the Bridge charges a service charge of $6.00 plus $1.80 per liter of diesel. In this case, we can model the cost of diesel by C(n) = 1.80n + 6.00, where C is the cost of the diesel in dollars and n is the number of liters. If the sailboat uses the gas station to fill up, what would be the domain for the equation, the range of costs, and the independent and dependent variables?arrow_forwarda satellite television company offers a 20% discount on the installation of any satellite television system. The company also advertises $50 in coupons for the cost of equipment. Find [c x d](x) and [d x c](x). Which composition of the coupon and discount results in the lower price? Explain.arrow_forward
- A scientist has a beaker containing 20 mL of a solution containing 20% acid. To dilute the acid, she adds pure water. An equation for the concentration in the beaker after adding n mL of water, C(n) , is 4 C(n) = 15 + n a. Find the new concentration (of acid) if 1 mL of water has been added. The new acid concentration will be at %. b. What is the behavior as n → 0 , and what is the physical significance of this? As n o0, C(п) — ? Your explanation for the physical meaning:arrow_forwardFind the solution: * (1+ y² + xy²)dx + (x²y + y + 2xy)dy = 0 a. 2x – y²(x + 1)2 = C b.2x?y? + (x + 1)² = carrow_forwardA company anticipates there will be a demand for 20,000 copies of a certain book during the next year/. It costs the company $0.50 to store a book for 1 year. Each time it must print additional books, it costs $200 to set up the equipment. NOTE: We assume that the demand is uniform. Let ⚫ x = number of books printed during each printing run ⚫ y = number of printing runsarrow_forward
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill