A) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 − 4q2 where q is the number of lightweight compasses produced in millions.It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? B) A virus is believed to be spreading through a sheep farm according to that equation N = 450 (1/1 + 249e−0.1t ) where N is the number of sheep infected and t is the number of days. (i) How many sheep are infected at t = 0?
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
A) You are the CEO for a lightweight compasses manufacturer. The demand
function for the lightweight compasses is given by p = 40 − 4q2 where q is the number of lightweight compasses produced in millions.It costs the company $15 to make a lightweight compass.
(i) Write an equation giving profit as a function of the number of lightweight compasses produced.
(ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?
B) A virus is believed to be spreading through a sheep farm according to that equation N = 450 (1/1 + 249e−0.1t ) where N is the number of sheep infected and t is the number of days.
(i) How many sheep are infected at t = 0?
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