The monthly income associated with the sale of two products is described with the function intwo variables / = 21a + 19b, where a and b are quantities sold of products A and B,respectively. Furthermore, it is known that the cost of producing these products is modeled byC = 3a² +6b². With this information answer:Write the criterion of the monthly profit function from the sales of products A and B, use asvariables a and bWhat is the only critical point of the utility function?What is the value of the discriminant of the utility function evaluated at that critical point(Value of D used to classify the critical point)At this critical point. Is a relative maximum, a relative minimum, or neither determined?

critical point ( maximum ,minimum or saddle point ) of a function occur accordingly fx (…

Answered: The monthly income associated with the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A grocery store sells two brands of a product, the "house" brand and a "name" brand. The manager estimates that if she sells the "house" brand for x dollars and the "name" brand for y dollars, she will be able to sell 63 – 10x + 21y units of the "house" brand and 40 + 13x – 10y units of the "name" brand. Step 1 of 2: Find the revenue function R(x, y).
Suppose that Alexander’s Coffee Shop has fixed costs of $18 and variable costs per unit of $4. The demand function for the coffee shop is P = 24 − 2Q. Given the demand and cost functions, calculate the maximum profit that Alexander’s Coffee Shop can earn.
If x represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c) state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of items), and (e) support the results of part (d) graphically. The fixed cost is $600, the cost to produce an item is $25, and the selling price of the item is $50. (a) The cost function is C(x) = (Simplify your answer. Do not factor.) (b) The revenue function is R(x)= (Simplify your answer. Do not factor.) (c) The profit function is P(x) = (Simplify your answer. Do not factor.) ← (d) At least items must be produced before a profit is shown. (Type a whole number.) (e) Choose the correct graph to the right. O A. 2100 O C. Dollars Items produced 2100 Items produced Q O B. 2100 O D. Dollars 2100 Items produced Items produced Q ✔
It costs a company $3,500 to produce 3,000 pencils whereas it costs the company $1,500a month even if they don't produce any pencils. If they sell the pencils for $0.75 and thecost, revenue, and profit functions are linear, determine how many pencils they must makein a month to break even
A firm sells a product for $80 per unit. Raw material costs are$12,50 per unit, labor costs are $27,50 per unit, and annual fixedcosts are $260,000.a. Determine the profit function P(x), where x equals the numberof units sold.b. How many units would have to be sold to earn an annualprofit of $250,000.
A company manufactures and sells x cell phones per week. The weekly price demand and cost functions are given respectively p(x) = 600 – 0.5x and C(x) = 20,000 + 130x. The maximum weekly profit is: A. $170,000. B. $81,100. C. $100,000. D. $90,450. Select one: O A O B O D
Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = X² X + 3 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) y² + 2Y + 9 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 5,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. min s.t. = X, Y Z 0 = 5 (b) Use Excel Solver or LINGO to find the solution to your mathematical model to determine the optimal…

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