Question

A toy store has shelf space to hold at most 60 baby dolls of three different types. Sleeping baby dolls cost $6 each, talking baby dolls cost $7.50 each, and walking baby dolls cost $9 each. The store can afford to spend up to $405 for the dolls. The sleeping, talking, and walking baby dolls resell for $12, $13.50, and $17 each, respectively. The store wishes to maximize its profit by ordering the appropriate number of each type of doll. (Remember: Profit = Revenue - Cost)

(a) How many of each type of doll should be ordered to maximize profit?

(b) What is the maximum profit?

Answer 1

Part a: The toy store should have 45 Sleeping baby dolls and 15 Walking baby dolls.

Part b: The maximum profit is $390

Step-by-step explanation:

Let the number of Sleeping baby dolls be X that of Talking baby dolls be Y and that of the Walking baby dolls be Z

Profits are given as

Profit of X=Selling Price-Cost=12-6=$6

Profit of Y=Selling Price-Cost=13.5-7.5=$6

Profit of Z=Selling Price-Cost=17-9=$8

So the Profit Function is

P=6X+6Y+8Z

Now the constraints are as

X+Y+Z≤60

Also

6X+7.5Y+9Z≤405

Using the excel sheet as indicated with the solution, the values of the X, Y and Z are calculated using the solver tool.

The data is as to be entered in the files attached and the solver is used such that The value of X is 45, Y is 0 and Z is 15.

The maximum profit is $390.

Answer 2

(a) To maximize profit, 45 sleeping baby dolls and 15 walking baby dolls should be ordered.

(b) The maximum profit is $390

Step-by-step explanation:

(a) The maximum number of dolls the shelf can hold is 60

Amount available to spend on the purchase of dolls is $405

Cost of 1 sleeping baby doll = $6

Cost of 45 sleeping baby dolls = 45 × $6 = $270

Cost of 1 walking baby doll = $9

Cost of 15 walking dolls = 15 × $9 = $135

Total cost of 45 sleeping and 15 walking baby dolls = $270 + $135 = $405

(b) Selling price of 1 sleeping baby doll = $12

Selling price of 45 sleeping baby dolls = 45 × $12= $540

Profit = $540 - $270 = $270

Selling price of 1 walking baby doll = $17

Selling price of 15 walking baby dolls = 15 × $17 = $255

Profit = $255 - $135 = $120

Maximum profit = $270 + $120 = $390