7&1. Answer question a & b Please show your steps/calculations and understanding steps by steps. a. You are in charge of marketing a new pair of sunglasses: The Ray Bob. For a sales cycle, it costs at the base $70,000, then $20 for each pair of glasses produced. When you set the price at $200 for a pair, you then sell 6,000 pairs. If you increase the price by $4, then you sell 4 pairs less. Let x be the number of pairs of glasses produced. I. Model the C(x) function of the cost of production. II. Model the p(x) function of the price per pair of glasses. III. Model the R(x) function of production revenue. IV. Model the P(x) function, of the profit of production. V. Find the value of x that maximizes profit. VI. Calculate P(x) the maximum profit. b. The campaign begins with a poster strategically placed in the middle of the campus. After 2 days, 11,500 students saw the poster, and it is expected that eventually, the entire student population (79,500 students) will be aware of the campaign. Let N(x) be the number of students who have seen the poster after x days since the beginning of the campaign, and suppose that the N(x) function is of the form: N(x) = Ca + k. I. Sketch the graph of the function N(x), which clearly includes N(0), N(2) and the horizontal asymptote. II. Model the N(x) function (find the equation). III. The Calvin Klein campaign wants to keep the poster until 50,000 students have seen the poster. How many days will Calvin Klein keep this poster on campus? So, calculate the value of x such as N(x)=50,000. Submit the answer below. The answer must be written in decimal places with 2 EXACT decimals of precision.
7&1.
Answer question a & b
Please show your steps/calculations and understanding steps by steps.
a.
You are in charge of marketing a new pair of sunglasses:
The Ray Bob. For a sales cycle, it costs at the base $70,000, then $20 for each pair of glasses produced. When you set the price at $200 for a pair, you then sell 6,000 pairs. If you increase the price by $4, then you sell 4 pairs less. Let x be the number of pairs of glasses produced.
I. Model the C(x) function of the cost of production.
II. Model the p(x) function of the price per pair of glasses.
III. Model the R(x) function of production revenue.
IV. Model the P(x) function, of the profit of production.
V. Find the value of x that maximizes profit.
VI. Calculate P(x) the maximum profit.
b.
The campaign begins with a poster strategically placed in the middle of the campus. After 2 days, 11,500 students saw the poster, and it is expected that eventually, the entire student population (79,500 students) will be aware of the campaign. Let N(x) be the number of students who have seen the poster after x days since the beginning of the campaign, and suppose that the N(x) function is of the form:
N(x) = Ca + k.
I. Sketch the graph of the function N(x), which clearly includes N(0), N(2) and the horizontal asymptote.
II. Model the N(x) function (find the equation).
III. The Calvin Klein campaign wants to keep the poster until 50,000 students have seen the poster. How many days will Calvin Klein keep this poster on campus? So, calculate the value of x such as N(x)=50,000.
Submit the answer below. The answer must be written in decimal places with 2 EXACT decimals of precision.
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