Math 100A
Modeling with Linear Functions II
Name:
1. Could the values in the table represent the values of a linear function? Explain.
t
Q
3
5.79
7
6.67
19
9.31
21
9.75
26
10.85
42
14.37
2. A gram of fat contains 9 dietary calories, whereas a gram of carbohydrates contains only 4.
(a) Write an equation relating the amount f , in grams, of fat and the amount c, in grams, of
carbohydrates that one can eat if limited to a total of 2000 calories/day.
(b) The USDA recommends that calories from fat should not exceed 30% of all calories. What
does this tell you about f ?
Math 100A
Modeling with Linear Functions II
3. Suppose you have $20 to spend on a barbecue. You go to Hy-Vee, and chicken costs $1.29/lb
and steak costs $3.49/lb.
(a) Write a constraint equation.
(b) Find two solutions.
(c) Graph the equation and mark your solutions.
y
✻
10
✲
−20
−10
10
−10
−20
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x
Math 100A
Modeling with Linear Functions II
4. A newly designed hotel has S small rooms measuring 250 ft2 and L large rooms measuring 400
ft2 . The designers have 10,000 ft2 of available space.
(a) Write an equation relating S to L.
(b) Sketch a graph of the equation from part (a).
L
✻
25
✲
−50
−25
25
S
−25
−50
(c) If the designers decide on 24 small rooms, how many larger rooms can they build? Find
your answer algebraically and graphically.
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Math 100A
Modeling with Linear Functions II
5. The final plans for the hotel in Question 4 call for a total floor space of 16,000 ft2 , and for
less spacious small rooms measuring 200 ft2 instead of 250 ft2 . Sketch a graph of the resulting
constraint equation in the plane in Question 4(b). How do the two graphs compare?
6. The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while Robusta yields
about 1200 kg/hectare. Suppose that a plantation has a hectares of Arabica and r hectares of
Robusta.
(a) Write an equation relating a and r if the plantation yields 1,000,000 kg of coffee.
(b) On August 14, 2003, the world market price of coffee was $1.42/kg for Arabica and $0.73/kg
for Robusta. Write an equation relating a and r if the plantation produces coffee worth
$1,000,000.
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