A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this pro

Question

A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 25 tons per day. The capacity for producing the product is 50 tons per day. Setup costs $100, and storage and handling costs are $8 per ton a year. The firm operates 200 days a year. (Note: 1 ton = 2,000 pounds.)

Here is the problem I am stuck on. I am getting lost on the last part of the problem. How do I calculate the savings?

a. How many bags per run are optimal? (Round your answer to the nearest whole number.)

Number of bags:

b. What would the average inventory be for this lot size? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)

Average inventory bags:

c. Determine the approximate length of a production run, in days. (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)

Run length days:

d. About how many runs per year would there be? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)

Run per year:

e. How much could the company save annually if the setup cost could be reduced to $33 per run?(Round your intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)

Savings:

Solution I get from the book is the following:

Where is the $1,148.93 coming from? How do I calculate TCrev?

Explanation: p = 50/ton/day u = 25 tons/day 200 days/yr. D = 25 tons/day times 200 days/yr. = 5,000 tons/yr. S = $100 H = $8/ton per yr. Q0 = 2DS/H p/p - u = 2(5,000) 100/8 50/25 = [500.00 tons times 20 = 10,000 bags] Imax = Q/P (p - u) = 500.00/50 (25) = 250.00 tons [250.00 tons times 20 = 5,000 bags] Average is Imax/2 = 250.00/2 = 125.00 tons [125.00 tons times 20 = 2,500 bags] Run length = Q/P = 500.00/50 = 10.00 days 10 Runs per year = D/Q = 5,000/500.00 = 10.00 10 Q' = 2DS/H p/p - u= 2(5,000)33/8 50/25 = 287.23 TC = Imax/2 H + D/Q S Savings = TCorig. - TCrev. =$2,000.00 - $1,148.93 =$851.07 Savings would be $851.07.

Explanation / Answer

e. How much could the company save annually if the setup cost could be reduced to $33 per run?(Round your intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)

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