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MakcuM [25]
3 years ago
11

Karen's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Karen $5.80 per pound, and type

B coffee costs $4.25 per pound. This month, Karen made 127 pounds of the blend, for a total cost of $657.55. How many pounds of type A coffee did she use?
Mathematics
1 answer:
Elina [12.6K]3 years ago
8 0

Answer:

76

Step-by-step explanation:

A + B = 127

5.80A + 4.25B = 657.55

Solve with substitution.

5.80A + 4.25(127 − A) = 657.55

5.80A + 539.75 − 4.25A = 657.55

1.55A = 117.80

A = 76

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Step-by-step explanation:

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The Best Company produces two commercial products : blenders and mixers. Both products require a two step production process inv
deff fn [24]

Answer:

Maximum profit is $87 when 3 blenders and 11 mixers are produced.

Step-by-step explanation:

let blender is represented by x_{1} and and mixer by x_{2}.

total time to deliver parts = 24 hrs

total time to assemble = 30 hrs

time taken by each blender to deliver parts = 1 hr

time taken by each mixer to deliver parts = 2 hr

time taken by blenders in final assembling= 2 hr

time taken by mixers in final assembling = 3 hr

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Each mixer produced nets the firm=  $6

Using this all data linear system of equation will be:

x_{1} + 2x_{2} =24  ----- (1)\\2x_{1} + 2x_{2} = 30 ----- (2)\\

profit function:

z= 7x_{1} +6x_{2} --- (3)

from (1)\\x_{1} = 0 \implies x_{2}= 12\\x_{2}= 0 \implies x_{1}= 24\\

Coordinate points obtained from (1) are (0,12) and (24,0)

from (2)\\x_{1}=0 \implies x_{2}=10\\x_{2}=0 \implies x_{1}=15\\

Coordinate points obtained from (2) are (0,10) and (15,0)

plotting these on graph

points lying in feasible region are:

A(0,0)

B(0,10)

C(3,11)

D(12,0)

substituting these points in (3) to find the maximum profit:

for A (0,0)

z = 0

for B (0,10)

z = 60

for C (3,11)

z =  87

for D (12,0)

z=84

So maximum profit is $87 when 3 blenders and 11 mixers are produced.

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