1. Consider the problem of a toy company that produces toy planes and toy boats. The toycompany can sell its planes for S10 and its boats for S8 dollars. A plane requires 3 hours to makeand 1 hour to finish while a boat requires 1 hour to make and 2 hours to finish. The toy companyknows it will not sell more than 35 planes per week. Further, given the number of workers, thecompany cannot spend more than 160 hours per week finishing toys and 120 hours per weekmaking toys. The company wishes to maximize the sales/revenue it makes by choosing howmuch of each toy to produce.A. Develop the linear programming model that maximizes sales/revenue.B. Use online graphing tool to determine the feasible solution. Take a screenshot of it.C. What are the corner points of the feasible region?D. How many of each type of toy must he produce to maximize sales/revenue? What is themaximum sales/revenue?PLANEВОАТREVENUE108ΤIΜE ΤΟ ΜΑΚΕ31120TIΜE ΤΟ FINISH12160

Let x be the number of planes and y be the number of boats The objective is to maximize the revenue…

Answered: 1. Consider the problem of a toy…

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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13) Z-Salon profits $12 on each manicure and $18 per haircut. A manicure takes 30 minutes and a haircut takes 50 minutes. There are 5 stylists who each work 6 hours per day (that is a total of 360 min x 5 = 1800 minutes in available labor). The salon can schedule 50 appointments per day. How many manicures and how many haircuts should be scheduled each day in order order to maximize profit? What is the maximum profit? Let’s get you started. Let x = number of manicures Let y = number of haircuts OBJECTIVE The objective (goal) is to maximize profit, P. So the objective equation is P = ______________________________________________ objective equation CONSTRAINTS: 1) 2) 3) 4) Now graph the above system of inequalities (constraints) on your graph paper: Find all vertices (corner points) of your shaded region. Plug them in one at a time into the objective. Note the one which makes P the biggest. This one is our solution. Corner Pt (x,y)…
6. A housing contractor designed two styles of houses – bungalows and 2-story houses for 100 available lots. The bungalows style requires P1.5M capital and produces a profit of P200,000 when sold. A 2-story house requires P2M capital and will earn a profit of P400,000. If the available capital on hand is P180M, how many houses of each type should be built to gain a maximum profit? Show your complete solution.
The owner of a condominium complex has 45 units all of which will be occupied if the rent charged is $600per month. The owner estimates that for every $20 increase in rent, one of the units will become vacant.The owner sets aside $60 per month from each of the occupied units to establish a repair fund. What rentshould be charged per month in order to maximize the owner’s profit if there are no other expenses? Whatis the owner’s maximum monthly profit? How many units are occupied?
14. If each unit of the product can be sold at a price of $5 and incurs variable costs which are constant at $3 per unit, and if the fixed costs already incurred are $15,000, then the number of units to break-even is: А. 15,000 units В. 3,000 units С. 5,000 units D. 7,500 units
The table below represents consumption along Edgar's budget constraint, with each row representing a possible consumption bundle. Edgar derives 50 unites of happiness from eating his first hot dog, 40 units for the recond hot dog, 30 unites for the third hot dog, and so on with added utility declining by 10 for each hot dog consumed. The first soda provides 30 unites and declines by steps iof 3 for each additional soda. Using this information identify the optional (highest utility) consumption for Edgar. Hot dogs Soda 0 10 1 8 2 6 3 4 4 2 5 0 a.) 2 hot dogs & 6 sodas b.) 1 hot dog & 8 sodas c.) 3 hot dogs & 4 sodas d.) 5 hot dogs & 0 sodas
5) A factory owner has 100 employees that produce 6000 computers per day. For each additional employee that the owner highers, the average production per employee decreases by 8 computers. How many employees should the owner have in order to maximize production?
4) PhotoMax makes disposable cameras that sell for $7.89 each and cost $3.24 each to produce. The weekly fixed cost for the company is $16500. a) Find equations for cost, revenue and profit functionsb) Graph each function on the same graph – indicate areas of profit and lossc) Find the break-even point
4. A manufacturer must decide how many chairs and tables to produce in a given week. It takes 2 hours to construct a chair and 3 hours to construct a table. The finishing process requires 2 hours for each chair and 2 hours for each table. There are 36 work hours available for construction and 28 work hours available for finishing. If the profit is $15 per chair and $25 per table, how many of each should be produced to maximize profit? Define your variables. HO 8 Find the Profit or Objective Function. Construction Find the Constraint equations. Do negatives make sense? 61 y Pt d for chairs for tables ho 21139036 X20 10 12 14 1618002 2 PCXIT ISXH59 The vertices of the feasible region. y 20 finish 2x+2y ≤28 Y= y=-2 3X+12
9. A company sells two types of shoes. The first uses 2 units of leather and 2 units of synthetic material and yields a profit of $8 per pair. The second type requires 5 units of leather and 1 unit of synthetic material and gives a profit of $10 per pair. If there are 40 units of leather and 16 units of synthetic material available, how many pairs of each type of shoe should be manufactured to maximize profit? What is the maximum profit?
A paper manufacturing company converts wood pulp to writing paper and newsprint. The profit on a unit of writing paper is $500 and the profit on a unit of newsprint is $350. Solve, a. Let x represent the number of units of writing paper produced daily. Let y represent the number of units of newsprint produced daily. Write the objective function that models total daily profit. b. The manufacturer is bound by the following constraints: * Equipment in the factory allows for making at most 200 units of paper (writing paper and newsprint) in a day. * Regular customers require at least 10 units of writingpaper and at least 80 units of newsprint daily. Write a system of inequalities that models these constraints. c. Graph the inequalitiers in part (b) Use only the first quadrant, because x and y must both be positive. (Suggestion: Let each unit along the x- and y-axes represent 20.) d. Evaluate the objective function at each of the three vertices of the graphed region. e. Complete the missing…
Suppose the demand functions faced by the monopolist firm are as follows: Q1 = 40 -2P1 + P2 Q2 = 15 + P1 – P2 Whereas, the cost function is given as : C = Q21 +Q1Q2 +Q22 Find the Maximum level of profit and also identify the optimal level of P1 and P2.
Refer to the production possibilities curves for Chairland and Tableland. Chairland can produce 36 chairs per day and no tables, or 18 tables table per day and no chairs. Tableland can produce 40 chairs per day and no tables, or 40 tables per day and no chairs. If the two countries split the difference between the buyer's willingness to pay for tables and the seller's willingness to accept, in terms of the number of chairs for 1 table, the terms of trade will be . (Enter your response rounded to one decimal place.) Country Quantity per day Opportunity cost of chairs Opportuity cost of tables Tableland 40 chairs, 40 tables 1 table 1 chair Chairland 36 chairs, 18 tables 1/2 table 2 chairs

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