A manufacturer of skis makes two types of skis: downhill and cross-country skis. The ski production process involves two steps: manufacturing and finishing. The manufacturing time is 3 hours per ski for downhill skis and 2 hours per ski for cross-country skis. The finishing time is 5 hours per ski for downhill skis and 2 hours per ski for cross-country skis. There are only 20 hours per week available for the manufacturing process and 25 hours for the finishing process. Due to existing sales contracts, at most 3 cross-country skis can be made for each downhill ski. The average profit is $43 for each downhill ski and $52 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit. (a) Identify and clearly define the variables needed to solve the linear programming problem. x= y= P= (b) Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your equation in the second answer blank. (Hint: Your equation must be written in the form P = , where the variable you are maximizing or minimizing is alone on one side of the equal sign.) (c) The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.) manufacturing time constraint finishing time constraint sales contracts constraint non-negativity constraints x≥0, y≥0

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 manufacturer of skis makes two types of skis: downhill and cross-country skis. The ski production process involves two steps: manufacturing and finishing. The manufacturing time is 3 hours per ski for downhill skis and 2 hours per ski for cross-country skis. The finishing time is 5 hours per ski for downhill skis and 2 hours per ski for cross-country skis.

There are only 20 hours per week available for the manufacturing process and 25 hours for the finishing process. Due to existing sales contracts, at most 3 cross-country skis can be made for each downhill ski. The average profit is $43 for each downhill ski and $52 for cross-country ski.

The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit.

(a)

Identify and clearly define the variables needed to solve the linear programming problem.

x= y= P=

(b)

Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your equation in the second answer blank. (Hint: Your equation must be written in the form P = , where the variable you are maximizing or minimizing is alone on one side of the equal sign.)

(c)

The objective function is subject to constraints. Determine the constraints below. (Hint: Write the constraints line by line. Separate the non-negativity constraints with commas.)

manufacturing time constraint

finishing time constraint

sales contracts constraint

non-negativity constraints

x≥0, y≥0

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