# problem solving

## Project Description:

1. solving for production cost for a firm. (round numbers to the nearest tenth.
tp tfc tvc tc afc avc atc mc
0 20 0 - - - - -
1 20 27.5
2 20 46.8
3 20 63.3
4 20 82.5
5 20 106.7
6 20 139.7
7 20 181

a. at what level of output do diminishing returns set in? how do you know?

2. profit maximization: ar, inc., operates in the highly competitive writing pens industry. prices for its q4 style features are stable at \$30 each. this means that p=mr=30 in the market. engineering estimates indicates that relevant total and marginal cost relations for the q4 model are:
tc =\$75,000+20q+\$0.00002q(2square)
mc= tc/q=20+\$0.00004q

a. calculate the output level that will maximize q4 profit.
b. calculate this maximum profit.

3. optimal price
last week peter burgers, inc.m reduced the average price on the 1/2-pound super burger by 1%. in response sales jumped by 4%.

a. calculate the point price elasticity of demand for size burgers.

b. calculate the optimal price for super burger

4. california grape farms inc. is a small grower of grapes. california grape farms estimates that grapes output would increase by 1,200 per month with an additional 1,000 gallons of water per month provided by irrigation system. alternatively, grapes output c could be increased by 500 per month with an additional 2 tons of fertilizer per month. assuming the cost of eater is \$.03 per gallon and fertilizer is \$25 per ton, is california grape farm using optimal combination of fertilizer and water (cost-minimizing combination of inputs? why or why not?

5. a monopolist has the marginal cost at \$60.
demand and marginal revenue equations are as follows:
qd=800-2p
mr=400-qd

find the profit-maximizing price and quantity of the monopolist firm.

include details of how problems were solved?
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Price Type: Negotiable

Completed
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