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# Calculating costs per swing sets.

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A company that specializes in making toys is currently making swing sets. To calculate the total cost per month for making the swings they use TC=81.6q - 01.04q^2 + 0.008q^3 in which q is the amount of swingsets produced in that same month.

a. Calculate the average cost per swing set with a monthly production of 50.

b. To calculate the average cost per month per swing set you can use the equation AC=0.008q^2 -1.04q + 81.6. Explain why.

c. Calculate q algebraically if the averge cost would be 72 euros.

d. Calculate algebraically with which montly production the average cost per swing set would be minimal.

Feb 19, 2020

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A company that specializes in making toys is currently making swing sets. To calculate the total cost per month for making the swings they use TC=81.6q - 01.04q^2 + 0.008q^3 in which q is the amount of swingsets produced in that same month.

a. Calculate the average cost per swing set with a monthly production of 50.

b. To calculate the average cost per month per swing set you can use the equation AC=0.008q^2 -1.04q + 81.6. Explain why.

c. Calculate q algebraically if the averge cost would be 72 euros.

d. Calculate algebraically with which montly production the average cost per swing set would be minimal.

a.  [ 81.6 (50)  - 1.04(50)^2  + .008(50^3 ]  / 50   =   49.6

b.   Note that    [ 81.6 q  - 1.04 q^2  + .008q^3 ]   / q   =

q [ 81.6 -1.04q  + .008q^2 ]  / q    =

81.6  -1.04q + .008q^2

c.  .008q^2 - 1.04q + 81.6  =  72

.008q^2  -1.04q  + 9.6   = 0        multiply through by 1000

8q^2 -1040q + 9600  = 0         divide through by 8

q^2  - 130q + 1200   = 0    factor

(q  - 120) (q - 10)   = 0

Set each factor to 0  and solve for q  and we have that  q =120   or  q  =10

d.  .008q^2  - 1.04q + 81.6

The q that   that  minimizes  the avg cost    =   -(-1.04)  / [ 2 * .008]  = 1.04 / .016  = 65  units

Feb 19, 2020