(a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (i) Derive an expression, R(q) for Teddy J's total revenue curve. (ii) Derive an expression, I(q) for Teddy J's profit function. (iii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![Problem 2
(a) The sales of a book publication are expected to grow according to the function
S= 300000(1-e-0.06t), where t is the time, given in days.
(i) Show using differentiation that the sales never attains an exact maximum value.
(ii) What is the limiting value approached by the sales function?
(b) A poll commissioned by a politician estimates that t days after he makes a statement
denegrating women, the percentage of his constituency (those who support him at the time he
75(t? – 3t + 25)
t2 + 3t + 25
made the statement) that still supports him is given by S(t) =
The election is 10 days after he made the statement.
(i) If the derivative S'(t) may be thought of as an approval rate, derivate the a function
for his approval rate.
(ii) When was his support at its lowest level?
(iii) What was his minimum support level?
(iv) Was the approval rate positive or negative on the date of the election?
(c) Lara offers 100 autograph bats. If each is priced at p dollars, it is that the demand curve
dq dp
for the bast will be p = 250 –. If price elasticily is E(p) =
When |E(p)| < 1,
demand is inelastic and when |E(p)| >1, demand is elastic.
(i) Find the price elasticity of demand for Lara's bats.
[5 mks]
(ii) Is demand inelastic or elastic?
[1 mk]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F372ca647-6830-4b40-84a6-45e8c0d5d6e0%2Fc32236af-f835-407c-bf84-6b8e5eb5e732%2Fhhsftz_processed.jpeg&w=3840&q=75)
The revenue is the total cost for p items (p is the same as given p, it might also be the quantity or some other value). Given that the demand function is given by while the total cost function is given by . To get the revenue function, we need to substitute the value of q in the cost function and get a function in terms of p. Therefore, we have solving which we get .
Hence, the required revenue function is given by .
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