A manufacturer of two products (Widgets and Gadgets) makes a profit of $180 for each widget sold and $100 for each gadget sold.However, production of these products generates hazardous waste charges at the rate of 1w (where Wis the number of Widgetsproduced) and 1o" (where Gis the number of Gadgets produced). The manufacturer has ample supplies of all raw materials and cansell all the Widgets and Gadgets it produces. The firm has sufficient capacity to produce any realistic quantity of both products.What is the optimal quantity of each product to produce? (Round your answers to 1 decimal place.)Widgets andGadgetsWhat is the maximum profit the manufacturer can earn? (Round your answer to 2 decimal places.)Mmum prott

Answered: Image /qna-images/answer/de204600-76fd-4c47-b7f2-7de7cc2dd5d3.jpg

Answered: manufacturer of two products (Widgets…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An automobile costs $20000 when sold brand new and depreciates at a rate of 10% per year. Which of the following equations models the value Vof the car tyears after being sold? O (t) = 20000(1.1)* OV(t) = 20000 – 0.10t O (t) = 20000 + 0.10t V(t) = 20000(0.9) OV(t) = 10 - 20000t Lr Ps hp
A manufacturing company has been experimenting with a new additive that is used to reduce polluting effluents from its production facility. Test results suggest that if no additive is used, pollution levels are 3000 parts per million (ppm). For each pound of additive used per week, pollution levels are reduced by 0.49 ppm. The additive costs $30 per pound. The reason for experimenting with the additive is that a government agency is conducting weekly air quality tests in the vicinity of the production facility. Regulations state that if pollution levels exceed 2000 ppm, a fine is imposed. The fine is $1000 for each ppm by which the pollution level exceeds the 2000 ppm limit. If the company has budgeted $80,000 per week to spend on the additive and any pollution fines, how much additive should be purchased each week for use by the company? What is the resulting amount that the company is willing to pay in terms of weekly fines?
Two connected tanks, each with a capacity of 50 liters, contain brine (saltwater). Initially, the first tank contains 18 liters of brine with a salt concentration of 3 grams per liter and the second contains 17 liters of brine with a salt concentration of 2 grams per liter. At t = 0 brine with a salt concentration of 6 grams per liter flows into the first tank at 8 liters per hour. Well-stirred brine flows from the first tank into the second at 7 liters per hour, from the second into the first at 5 liters per hour, from the first into a drain at 4 liters per hour, and from the second into a drain at 3 liters per hour. (a) Determine the volume (liters) of brine in each tank as a function of time.(b) Give an initial-value problem that governs the amount (grams) of salt in eachtank as a function of time.(c) Give the interval of definition for the solution of this initial-value problem.
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The demand equation for a certain product is 6p² + q² = 1,200, where p is the price per unit in dollars and q is the number of units demanded. Find dq/dp. OA. dq/dp - p/6q OB. dq/dp - 6p/q OC. dq/dp -q/6p OD. dq/dp - 6q/p ...
A company sells its product at 60 OMR per unit. The fixed cost is 19500 OMR, and the variable cost is estimated to be 35% of the total revenue, then the brake-even point is Select one: O a. 800 O b. 500 O c. 1000 O d. 780
The monthly demand for Williams Tchotchkes (q measured in 1000s of tchotchkes) depends on the price that they set for their tchotchkes (p measured in dollars), the average price of substitutes for their tchotchkes (p, also measured in dollars), and the average monthly disposable income in the market for tchotchkes (y measured in $1000s). The current prices are p = $10 and p₁ = $11, the current monthly demand for Williams Tchotchkes is 8000 tchotchkes and the current average monthly disposable income in the tchotchkes market is $3500. Furthermore, it is known that Əq Op p=10 Pg=11 y=3.5 = -0.31, Əq aps P=10 Pg=11 y=3.5 = 0.44 and Əq dy p=10 Pg=11 y=3.5 = 0.72. Scenario 1: Suppose that p increases by $0.20, p, increases by $0.35 (from their current values), and income doesn't change. In this scenario, monthly demand for Williams Tchotchkes' monthly will [Select] , and Williams Tchotchkes' monthly revenue will [Select] Scenario 2: Now (instead) suppose that average monthly income in the…
rials eo uations ow....zip Process . @ 2 D W Yaster Outfitters manufactures and sells extreme-cold sleeping bags. The table below shows the price-demand and total cost data, where: D • p is the wholesale price (in dollars) of a sleeping bag for a weekly demand of a sleeping bags; . C is the total cost (in dollars) of producing a sleeping bags. x (sleeping bags) p ($) 95 240 235 155 50 120 180 220 Use this data to create regression models to answer all of the questions below. #3 Price Model Find a quadratic regression equation for the price-demand data, using a as the independent variable. E p=a+bx+cr² Round a to the nearest integer, round b to 2 decimal places, and round c to 4 decimal places. Use this price model to answer question 1-2 below. $ 4 5 6 MacBook Pro C ($) 13,000 14,300 18,500 21,000 Y PEAR & * 8 ( 9 0 0 P A
A manufacturer's total production of a new product is P(L, K) = 1800L2/3K1/3 where L is the number of units of labor and K is the number of units of capital. A unit of labor costs $200, a unit of capital $800, and the total budget for labor and capital is $960,000. (a) To maximize production, how much should be spent on labor? 2$ How much on capital? 24 (b) Find the value of the Lagrange multiplier. Give an interpretation of the Lagrange multiplier. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in labor, L, by one unit. O The Lagrange multiplier is the approximate increase in the total budget for labor and capital resulting from an increase in the optimal value of P by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting from an increase in the total budget for labor and capital by one unit. O The Lagrange multiplier is the approximate increase in the optimal value of P resulting…

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