A company produces two models of a surfboard: a standard model and a competition model. If the standard model is produced at a variable cost of $240 each and the competition model at a variable cost of $330 each, and if the total fixed costs per month are $4 comma 000, then the monthly cost function is given by Upper C (x comma y )equals 4 comma 000 plus 240 x plus 330 y where x and y are the numbers of standard and competition models produced per month, respectively. Find C(24,12), C(70,7), and C(30,30).

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warylucknow warylucknow · Answer 1 · 2020-05-16T07:58:22+02:00

Answer:

(1) C (24, 12) = $13,720

(2) C (70, 7) = $23,110

(3) C (30, 30) = $21,100

Step-by-step explanation:

The monthly cost function for the production of two models of a surfboard, a standard model and a competition model is:

[tex]C(x,\ y)=4000+240x+330y[/tex]

Here,

x = number of standard model surfboard produced per month

y = number of competition model surfboard produced per month

(1)

Compute the value of C (24, 12) as follows:

[tex]C(x,\ y)=4000+240x+330y[/tex]

[tex]C(24,\ 12)=4000+(240 \cdot24)+ (330\cdot12)[/tex]

[tex]=4000+5760+3960\\=13720[/tex]

Thus, the monthly cost of producing 24 standard model and 12 competition model surfboard per month is $13,720.

(2)

Compute the value of C (70, 7) as follows:

[tex]C(x,\ y)=4000+240x+330y[/tex]

[tex]C(70,\ 7)=4000+(240 \cdot70)+ (330\cdot7)[/tex]

[tex]=4000+16800+2310\\=23110[/tex]

Thus, the monthly cost of producing 70 standard model and 7 competition model surfboard per month is $23,110.

(3)

Compute the value of C (30, 30) as follows:

[tex]C(x,\ y)=4000+240x+330y[/tex]

[tex]C(30,\ 30)=4000+(240 \cdot30)+ (330\cdot30)[/tex]

[tex]=4000+7200+9900\\=21100[/tex]

Thus, the monthly cost of producing 30 standard model and 30 competition model surfboard per month is $21,100.