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.
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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
