7. PRODUCTION A glass blower can form 8 simple vases or 2 elaborate vases in an hour. In a
work shift of no more than 8 hours, the worker must form at least 40 vases.
a. Lets represent the hours forming simple vases and e the hours forming elaborate vases.
Write a system of inequalities involving the time spent on each type of vase.
b. If the glass blower makes a profit of $30 per hour worked on the simple vases and $35
per hour worked on the elaborate vases, write a function for the total profit on the vases.
c. Find the number of hours the worker should spend on each type of vase to maximize
profit. What is that profit?

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sonu36 sonu36 · Answer 1 · 2019-11-07T10:40:36+01:00

Answer:

a)[tex] x >= 4 [/tex] , [tex] y <= 4 [/tex]

b)[tex] 280 - 5 \times x [/tex]

c) x = 4, y = 4 , $ 260

Step-by-step explanation:

a)Let, the glass bowler works for x hours on simple vases and y hours on elaborate vases.

According to the question,

[tex] y = 8 -x [/tex] -----------(1)

Also, the glass blower has to make at least 40 vases in 8 hours.

So,

[tex]8 \times x + 2 \times (8 - x) >= 40 [/tex]

⇒ [tex]6 \times x >= 24 [/tex]

⇒[tex] x >= 4 [/tex] ---------(1)

⇒[tex] 8 - x <= 4 [/tex]

⇒[tex] y <= 4 [/tex]----------(2)

b)Again profit of the glass blower, ( in $)

= [tex] 30 \times x + 35 \times (8 - x) [/tex]

= [tex] 280 - 5 \times x [/tex]--------------(2)

which will be maximum when x is minimum which is 4 (from (1))

so [tex] y = 8 -x = 4 [/tex]

and the profit is,

[tex] (280 - 5 \times 4)[/tex] (in $)

=$ 260