3. A business sells computer hardware (H) and software (S). The hardware sells f

Question

3. A business sells computer hardware (H) and software (S). The hardware sells for $70 and the software sells for $50. The total cost of selling these two goods is represented by this equation: TC = H2 + HS + S2 Find the maximum profit for this business, and the values of hardware and software where this is achieved. 5 marks Your company manufactures nuts (N) and bolts (B). Find the number of nuts and bolts that maximizes profit given the below profit function and constraint. What is the profit at this value? 5 marks 4. Profit = N + 2N B Constraint: 5 = N + 2B

Explanation / Answer

Question 3

TC = H2 + HS + S2

Calculate the marginal cost of producing computer hardware (H) -

MC(H) = dTC/dH = d(H2 + HS + S2)/dH = 2H + S

Calculate the marginal cost of producing computer software (S) -

MC(S) = dTC/dS = d(H2 + HS + S2)/dS = H + 2S

Price of hardware (H) = $70

Price of software (S) = $50

Equating MC(H) and P(H) to ascertain optimum quantity of hardware -

2H + S = 70          ---Equation (1)

Equating MC(S) and P(S) to ascertain optimum quantity of software -

H + 2S = 50         ---Equation (2)

Solving equation (1) and (2),

S = 10

H = 30

Calculate Profit -

Profit = TR - TC

Profit = {[P(H) * Q(H)] + [P(S) * Q(S)]} - [H2 + HS + S2]

Profit = [(70 * 30) + (50 * 10)] - [302 + (30*10) + 102]

Profit = $1,300

The maximum profit is $1,300

The values of hardware and software that achieve this are -

Hardware = 30 units

Software = 10 units

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