34. A computer salesman will order two new types of computers. He has a budget of at most €80 000 and a storage capacity of at most 300 m³. He buys computers of type 1 at a price of €400 per unit and computers of type 2 at €200 per unit. A computer of type 1 takes up 0.75 m³ of storage space, whereas a computer of type 2 takes up 1 m³. You can assume that both types of computers can be stored together without loss of space. On a computer of type 1 the salesman makes a profit of €300, on a computer of type 2 he makes a profit of €450. He wants to make a total profit of at least €45 000. You can assume that all computers that are bought can be sold. (a) Show on a graph which combinations of computers of type 1 and type 2 satisfy all the conditions mentioned. (b) Explain how one can read from the graph which of these combinations yields maximal profit. Determine this combination. Assume now that an order needs to contain at least twice as many computers of type 1 as of type 2. (c) Show on the graph you made in part a which combinations of computers of type 1 and type 2 satisfy this supplementary condition as well as the original conditions. (d) Which of the combinations that satisfy this supplementary condition as well as the original conditions. vields maximal profit?
34. A computer salesman will order two new types of computers. He has a budget of at most €80 000 and a storage capacity of at most 300 m³. He buys computers of type 1 at a price of €400 per unit and computers of type 2 at €200 per unit. A computer of type 1 takes up 0.75 m³ of storage space, whereas a computer of type 2 takes up 1 m³. You can assume that both types of computers can be stored together without loss of space. On a computer of type 1 the salesman makes a profit of €300, on a computer of type 2 he makes a profit of €450. He wants to make a total profit of at least €45 000. You can assume that all computers that are bought can be sold. (a) Show on a graph which combinations of computers of type 1 and type 2 satisfy all the conditions mentioned. (b) Explain how one can read from the graph which of these combinations yields maximal profit. Determine this combination. Assume now that an order needs to contain at least twice as many computers of type 1 as of type 2. (c) Show on the graph you made in part a which combinations of computers of type 1 and type 2 satisfy this supplementary condition as well as the original conditions. (d) Which of the combinations that satisfy this supplementary condition as well as the original conditions. vields maximal profit?
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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could you please write it with pen and paper? i appreciate it
Transcribed Image Text:34. A computer salesman will order two new types of computers. He has a budget of at most €80 000
and a storage capacity of at most 300 m³. He buys computers of type 1 at a price of €400 per unit
and computers of type 2 at €200 per unit. A computer of type 1 takes up 0.75 m³ of storage space,
whereas a computer of type 2 takes up 1 m³. You can assume that both types of computers can
be stored together without loss of space. On a computer of type 1 the salesman makes a profit of
€300, on a computer of type 2 he makes a profit of €450. He wants to make a total profit of at least
€45 000. You can assume that all computers that are bought can be sold.
(a) Show on a graph which combinations of computers of type 1 and type 2 satisfy all the conditions
mentioned.
(b) Explain how one can read from the graph which of these combinations yields maximal profit.
Determine this combination.
Assume now that an order needs to contain at least twice as many computers of type 1 as of type 2.
(c) Show on the graph you made in part a which combinations of computers of type 1 and type 2
satisfy this supplementary condition as well as the original conditions.
(d) Which of the combinations that satisfy this supplementary condition as well as the original
conditions, yields maximal profit?
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