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Unformatted text preview: ﬁg; American University of Sharjah MTH 101 — Mathematics For Business 1
Fall 2007 11th Edition solutions to the selected problems of section 12 Solutions by Omar Adnan Al Ismail Question 5 9: Fixed costs = $124/day
Variable costs = $0.12/doughnut
Number of doughnuts produced = x
A) Find the daily cost function C(x).
Total cost = Fixed costs + Variable costs
= PC + (VC per doughnut. Number of doughnuts produced)
= 124 + 0.12 x
B) Find the number of doughnuts produced if the total cost was $250
C(x) = 250
250 = 124 + 0.12 x
250  124 = 0.12 x
X = 1050 doughnuts can be produced for the cost of $250 Question 61 (Graded): Number of _olf clubs/ da
_ $7,647
$9,147 A)Find the cost function C00 333’ C(x2)— C(xl) 9147—7547 1500
S Ope Ax xz—xl 10080 20 5 C(x) = 75 x + b
7647 = 75 (80) + b
B = 1647
C(x) = 75 x + 1647
B) Graph the function C(x) where 0 S x S 200 17500 15000 12500 10000
7500
5000 2500 IIJIIIIIII:
25 so 15 100 125 150 115 200 225 250 Question 63: Scum Price R x
$112
$175 $238 A)Find the Selling Price Function R(x) _ _ Ay _ chz)— R(x1) _ 238—112 _
m 510136 Ax xzxl 175—85 _ 1'4 R(x) = 1.4 x + b
112 = 1.4 (85) + b
B=7 C(x) = 1.4x — 7
B)Find the cost of a product with a selling price of $185.
C(x) = 185
185 = 1.4x  7
185 + 7 = 1.4x
x x $137 Question 65 (Graded): Tractor’s Value V t
_ $157,000
$82,000 A)Find the tractor’s value function in terms of t years. 111 ___ slope = n_y = V(t2)— V(t1) = 232,000—157,000 = _7500 Ax tz—tl 10—0
V(t) = —7500 t + b
y  intercept = 157,000
V(t) = —7500 t + 157000
B) Find the tractor’s value after 6 year. V(6) = —7500 (6) + 157000 = $112,000 C) After how many years will the tractor has a value less than $7000?
V(t) = 7000
7000 = —7500 t + 157000
t= 11.6 years D)Graph V(t) where 0 S t S 20 Y 350000 — —
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159mm ‘— — 108000 ' L 50000 — — Question 75: 7.500 7.900
7.900 7,800 0 Find the pricesupply equation m = slope = A—y = —P(x2)" P("1)= —2'37'”8 = 0.000225 Ax x2 x1 7900—7500 P(x) = 0.000225 x + b 2.28 = 0.000225 (7500) + b
B = 0.5925 P(x) = 0.000225 x + 0.5925 0 Find the pricedemand equation Ay _ P(x2)— p(x1) _ 2.37—2.28 m = slope =————— = —0.0009 P(x) = —0.0009 x + b
2.28 = —0.0009 (7900) + b
B = 9.39
P(x) = — 0.0009 x + 9.39
0 Find the equilibrium point.
0.000225 x + 0.5925 = —0.0009 x + 9.39
x = 7820, p(x) = 2.352 The point: (7820, 2.352) 0 Graph the supply and demand functions 5‘! ‘ '"'l"l"'l"'
4.5— X
. I . . . l . . . I . . . i . . . I . . . . . .  . . '.
2000 4000 0000 3000 10000 12000 14000 ...
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 Fall '08
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