Question

Q-7      A company sells its two products A and B. The prices of products A and B are $5 and $8 per unit respectively. The material costs for A and B are $0.5 and $1.5 per unit respectively. The labour charges of $0.5 per unit is same for both of the products A and B. The fixed cost of the business is estimated as $3000.

1. Formulate the total revenue function if x1 and x2 units are sold of product A and B respectively.
2. Formulate the total cost function if x1 and x2 units are produced of product A and B respectively.
3. Formulate the total profit function if x1 and x2 units are produced and sold of product A and B respectively.
4. Calculate the total profit if 50,000 units of product A and 80,000 units of product B are produced and sold.

Answer 1

Price of A ( p1) = $5

Price of B (p2) = $8

Quantity of A = x1

Quantity of B = x2

Total Revenue Formula = Price * Quantity Sold

a. Therefore, Total Revenue function will be

= p1 *x1 + p2 * x2

= $5x1 + $8x2

b. Total Cost Formula = Total variable cost + Total fixed cost

Now, Product A units = x1

Material Cost per unit ( m1) = $0.5

Labour cost per unit ( l1)= $ 0.5

Variable cost of product A units = ( m1 +l1) * number of units produced

= ($0.5+$0.5) * x1

= $ 1x1

Product B units = x2

Material cost per units= $1.5

Labour cost per unit= $0.5

Variable cost of product B = ($1.5+$0.5)*x2

    =$2.0x2

Therefore

Total cost function = V(A+B) + Fixed Cost

= ($1.0x1 + $2.0x2) + $ 3000

c. Total Profit = Total Revenue - Total Cost

So, Total Profit function will be

= $5x1 +$8x2 -[($1x1 +$2x2) +$3000]

=$4x1+$6x2-$3000

d. Units of Product A = 50000

Units of Product B = 80000

Then Total Profit = $4*50000 +$6*80000-$3000

=$677000