Answer to Question #212315 in Economics for bumnan

Question

 4. Winthorp Printing Company has estimated the cost of making new brochures for one of its major clients as follows: an initial cost of $2,500, $3 per brochures for the first 5,000 brochures, $2 per brochure for the next 10,000 brochures and $1.50 per brochure for any brochure in excess of 15,000. i. Determine the cost function and graph it. ii. What are the total and average costs of 4,000 brochures ?. iii. Of 4,000 brochures ? iv. Of 4,000 brochures ?

v. How many brochures were printed if the total charge was $ 60,000 ? vi. How many brochures were printed if the average charge was $ 2.75 ?

Answer 1

i. The cost function is:

TC = 2,500

+ 3Q {0 < Q <= 5,000}

+ 2Q {5,000 < Q <= 15,000}

+ 1.5Q {Q > 15,000}

ii. The total and average costs of 4,000 brochures are:

TC = 2,500 + 3*4,000 = 14,500,

ATC = 14,500/4,000 = 3.625.

iii. TC = 2,500 + 3*4,000 = 14,500,

ATC = 14,500/4,000 = 3.625.

iv. TC = 2,500 + 3*4,000 = 14,500,

ATC = 14,500/4,000 = 3.625.

v. If the total charge was $ 60,000, then:

2,500 + 1.5Q = 60,000,

1,5Q = 57,500,

Q = 38,333.33.

vi. If the average charge was $ 2.75, then:

2,500/Q + 2 = 2.75,

0.75Q = 2,500,

Q = 3,333.33.